---
_id: '33333'
author:
- first_name: Andi Q.
  full_name: Wang, Andi Q.
  last_name: Wang
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Gareth O.
  full_name: Roberts, Gareth O.
  last_name: Roberts
- first_name: David
  full_name: Steinsaltz, David
  last_name: Steinsaltz
citation:
  ama: Wang AQ, Kolb M, Roberts GO, Steinsaltz D. Theoretical properties of quasi-stationary
    Monte Carlo methods. <i>The Annals of Applied Probability</i>. 2019;29(1). doi:<a
    href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>
  apa: Wang, A. Q., Kolb, M., Roberts, G. O., &#38; Steinsaltz, D. (2019). Theoretical
    properties of quasi-stationary Monte Carlo methods. <i>The Annals of Applied Probability</i>,
    <i>29</i>(1). <a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>
  bibtex: '@article{Wang_Kolb_Roberts_Steinsaltz_2019, title={Theoretical properties
    of quasi-stationary Monte Carlo methods}, volume={29}, DOI={<a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>},
    number={1}, journal={The Annals of Applied Probability}, author={Wang, Andi Q.
    and Kolb, Martin and Roberts, Gareth O. and Steinsaltz, David}, year={2019} }'
  chicago: Wang, Andi Q., Martin Kolb, Gareth O. Roberts, and David Steinsaltz. “Theoretical
    Properties of Quasi-Stationary Monte Carlo Methods.” <i>The Annals of Applied
    Probability</i> 29, no. 1 (2019). <a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>.
  ieee: 'A. Q. Wang, M. Kolb, G. O. Roberts, and D. Steinsaltz, “Theoretical properties
    of quasi-stationary Monte Carlo methods,” <i>The Annals of Applied Probability</i>,
    vol. 29, no. 1, 2019, doi: <a href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>.'
  mla: Wang, Andi Q., et al. “Theoretical Properties of Quasi-Stationary Monte Carlo
    Methods.” <i>The Annals of Applied Probability</i>, vol. 29, no. 1, 2019, doi:<a
    href="http://dx.doi.org/10.1214/18-AAP1422">http://dx.doi.org/10.1214/18-AAP1422</a>.
  short: A.Q. Wang, M. Kolb, G.O. Roberts, D. Steinsaltz, The Annals of Applied Probability
    29 (2019).
date_created: 2022-09-12T07:24:52Z
date_updated: 2022-09-12T07:32:35Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/18-AAP1422
intvolume: '        29'
issue: '1'
language:
- iso: eng
publication: The Annals of Applied Probability
status: public
title: Theoretical properties of quasi-stationary Monte Carlo methods
type: journal_article
user_id: '85821'
volume: 29
year: '2019'
...
---
_id: '33334'
abstract:
- lang: eng
  text: In the present work we characterize the existence of quasistationary distributions
    for diffusions on (0,∞) allowing singular behavior at 0 and ∞. If absorption at
    0 is certain, we show that there exists a quasistationary distribution as soon
    as the spectrum of the generator is strictly positive. This complements results
    of Collet et al. and Kolb/Steinsaltz for 0 being a regular boundary point and
    extends results by Collet et al. on singular diffusions. We also study the existence
    and uniqueness of quasistationary distributions for a class of one-dimensional
    diffusions with killing that arise from a biological example and which have two
    inaccessible boundary points (more specifically 0 is natural and ∞ is entrance).
author:
- first_name: Alexandru
  full_name: Hening, Alexandru
  last_name: Hening
- first_name: Martin
  full_name: Kolb, Martin
  last_name: Kolb
citation:
  ama: Hening A, Kolb M. Quasistationary distributions for one-dimensional diffusions
    with two singular boundary points. <i>Stochastic Processes and their Applications</i>.
    2019;129(5):1659-1696. doi:<a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>
  apa: Hening, A., &#38; Kolb, M. (2019). Quasistationary distributions for one-dimensional
    diffusions with two singular boundary points. <i>Stochastic Processes and Their
    Applications</i>, <i>129</i>(5), 1659–1696. <a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>
  bibtex: '@article{Hening_Kolb_2019, title={Quasistationary distributions for one-dimensional
    diffusions with two singular boundary points}, volume={129}, DOI={<a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>},
    number={5}, journal={Stochastic Processes and their Applications}, publisher={Bernoulli
    Society for Mathematical Statistics and Probability}, author={Hening, Alexandru
    and Kolb, Martin}, year={2019}, pages={1659–1696} }'
  chicago: 'Hening, Alexandru, and Martin Kolb. “Quasistationary Distributions for
    One-Dimensional Diffusions with Two Singular Boundary Points.” <i>Stochastic Processes
    and Their Applications</i> 129, no. 5 (2019): 1659–96. <a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>.'
  ieee: 'A. Hening and M. Kolb, “Quasistationary distributions for one-dimensional
    diffusions with two singular boundary points,” <i>Stochastic Processes and their
    Applications</i>, vol. 129, no. 5, pp. 1659–1696, 2019, doi: <a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>.'
  mla: Hening, Alexandru, and Martin Kolb. “Quasistationary Distributions for One-Dimensional
    Diffusions with Two Singular Boundary Points.” <i>Stochastic Processes and Their
    Applications</i>, vol. 129, no. 5, Bernoulli Society for Mathematical Statistics
    and Probability, 2019, pp. 1659–96, doi:<a href="http://dx.doi.org/10.1016/j.spa.2018.05.012">http://dx.doi.org/10.1016/j.spa.2018.05.012</a>.
  short: A. Hening, M. Kolb, Stochastic Processes and Their Applications 129 (2019)
    1659–1696.
date_created: 2022-09-12T07:46:44Z
date_updated: 2022-09-12T07:46:47Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1016/j.spa.2018.05.012
intvolume: '       129'
issue: '5'
language:
- iso: eng
page: 1659-1696
publication: Stochastic Processes and their Applications
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
status: public
title: Quasistationary distributions for one-dimensional diffusions with two singular
  boundary points
type: journal_article
user_id: '85821'
volume: 129
year: '2019'
...
---
_id: '33335'
abstract:
- lang: eng
  text: For a class of one-dimensional autoregressive sequences (Xn), we consider
    the tail behaviour of the stopping time T0=min{n≥1:Xn≤0}. We discuss existing
    general analytical approaches to this and related problems and propose a new one,
    which is based on a renewal-type decomposition for the moment generating function
    of T0 and on the analytical Fredholm alternative. Using this method, we show that
    Px(T0=n)∼V(x)Rn0 for some 0<R0<1 and a positive R0-harmonic function V. Further,
    we prove that our conditions on the tail behaviour of the innovations are sharp
    in the sense that fatter tails produce non-exponential decay factors.
author:
- first_name: Günter
  full_name: Hinrichs, Günter
  last_name: Hinrichs
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Vitali
  full_name: Wachtel, Vitali
  last_name: Wachtel
citation:
  ama: Hinrichs G, Kolb M, Wachtel V. Persistence of one-dimensional AR(1)-processes.
    <i>Journal of Theoretical Probability</i>. 2018;33:65–102. doi:<a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>
  apa: Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2018). Persistence of one-dimensional
    AR(1)-processes. <i>Journal of Theoretical Probability</i>, <i>33</i>, 65–102.
    <a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>
  bibtex: '@article{Hinrichs_Kolb_Wachtel_2018, title={Persistence of one-dimensional
    AR(1)-processes}, volume={33}, DOI={<a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>},
    journal={Journal of Theoretical Probability}, publisher={Springer Science + Business
    Media}, author={Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2018},
    pages={65–102} }'
  chicago: 'Hinrichs, Günter, Martin Kolb, and Vitali Wachtel. “Persistence of One-Dimensional
    AR(1)-Processes.” <i>Journal of Theoretical Probability</i> 33 (2018): 65–102.
    <a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.'
  ieee: 'G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of one-dimensional AR(1)-processes,”
    <i>Journal of Theoretical Probability</i>, vol. 33, pp. 65–102, 2018, doi: <a
    href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.'
  mla: Hinrichs, Günter, et al. “Persistence of One-Dimensional AR(1)-Processes.”
    <i>Journal of Theoretical Probability</i>, vol. 33, Springer Science + Business
    Media, 2018, pp. 65–102, doi:<a href="https://link.springer.com/article/10.1007/s10959-018-0850-0">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.
  short: G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018)
    65–102.
date_created: 2022-09-12T07:50:38Z
date_updated: 2022-09-12T07:52:44Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s10959-018-0850-0
intvolume: '        33'
language:
- iso: eng
page: 65–102
publication: Journal of Theoretical Probability
publication_status: published
publisher: Springer Science + Business Media
status: public
title: Persistence of one-dimensional AR(1)-processes
type: journal_article
user_id: '85821'
volume: 33
year: '2018'
...
---
_id: '33336'
abstract:
- lang: eng
  text: The dipole approximation is employed to describe interactions between atoms
    and radiation. It essentially consists of neglecting the spatial variation of
    the external field over the atom. Heuristically, this is justified by arguing
    that the wavelength is considerably larger than the atomic length scale, which
    holds under usual experimental conditions. We prove the dipole approximation in
    the limit of infinite wavelengths compared to the atomic length scale and estimate
    the rate of convergence. Our results include N-body Coulomb potentials and experimentally
    relevant electromagnetic fields such as plane waves and laser pulses.
author:
- first_name: Lea
  full_name: Boßmann, Lea
  last_name: Boßmann
- first_name: Robert
  full_name: Grummt, Robert
  last_name: Grummt
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Boßmann L, Grummt R, Kolb M. On the dipole approximation with error estimates.
    <i>Letters in Mathematical Physics</i>. 2017;108:185–193. doi:<a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>
  apa: Boßmann, L., Grummt, R., &#38; Kolb, M. (2017). On the dipole approximation
    with error estimates. <i>Letters in Mathematical Physics</i>, <i>108</i>, 185–193.
    <a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>
  bibtex: '@article{Boßmann_Grummt_Kolb_2017, title={On the dipole approximation with
    error estimates}, volume={108}, DOI={<a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>},
    journal={Letters in Mathematical Physics}, author={Boßmann, Lea and Grummt, Robert
    and Kolb, Martin}, year={2017}, pages={185–193} }'
  chicago: 'Boßmann, Lea, Robert Grummt, and Martin Kolb. “On the Dipole Approximation
    with Error Estimates.” <i>Letters in Mathematical Physics</i> 108 (2017): 185–193.
    <a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>.'
  ieee: 'L. Boßmann, R. Grummt, and M. Kolb, “On the dipole approximation with error
    estimates,” <i>Letters in Mathematical Physics</i>, vol. 108, pp. 185–193, 2017,
    doi: <a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>.'
  mla: Boßmann, Lea, et al. “On the Dipole Approximation with Error Estimates.” <i>Letters
    in Mathematical Physics</i>, vol. 108, 2017, pp. 185–193, doi:<a href="https://link.springer.com/article/10.1007/s11005-017-0999-y">https://link.springer.com/article/10.1007/s11005-017-0999-y</a>.
  short: L. Boßmann, R. Grummt, M. Kolb, Letters in Mathematical Physics 108 (2017)
    185–193.
date_created: 2022-09-12T08:08:05Z
date_updated: 2022-09-12T08:08:09Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s11005-017-0999-y
intvolume: '       108'
language:
- iso: eng
page: 185–193
publication: Letters in Mathematical Physics
publication_status: published
status: public
title: On the dipole approximation with error estimates
type: journal_article
user_id: '85821'
volume: 108
year: '2017'
...
---
_id: '33342'
abstract:
- lang: eng
  text: In this work we consider a one-dimensional Brownian motion with constant drift
    moving among a Poissonian cloud of obstacles. Our main result proves convergence
    of the law of processes conditional on survival up to time t as t converges to
    infinity in the critical case where the drift coincides with the intensity of
    the Poisson process. This complements a previous result of T. Povel, who considered
    the same question in the case where the drift is strictly smaller than the intensity.
    We also show that the end point of the process conditioned on survival up to time
    t rescaled by √t converges in distribution to a non-trivial random variable, as
    t tends to infinity, which is in fact invariant with respect to the drift h>0.
    We thus prove that it is sub-ballistic and estimate the speed of escape. The latter
    is in a sharp contrast with discrete models of dimension larger or equal to 2
    when the behaviour at criticality is ballistic, see [7], and even to many one
    dimensional models which exhibit ballistic behaviour at criticality, see [8].
author:
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Savov M, Kolb M. Conditional survival distributions of Brownian trajectories
    in a one dimensional Poissonian environment in the critical case. <i>Electronic
    Journal of Probability</i>. 2017;22. doi:<a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>
  apa: Savov, M., &#38; Kolb, M. (2017). Conditional survival distributions of Brownian
    trajectories in a one dimensional Poissonian environment in the critical case.
    <i>Electronic Journal of Probability</i>, <i>22</i>. <a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>
  bibtex: '@article{Savov_Kolb_2017, title={Conditional survival distributions of
    Brownian trajectories in a one dimensional Poissonian environment in the critical
    case}, volume={22}, DOI={<a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>},
    journal={Electronic Journal of Probability}, publisher={ Institute of Mathematical
    Statistics &#38; Bernoulli Society}, author={Savov, Mladen and Kolb, Martin},
    year={2017} }'
  chicago: Savov, Mladen, and Martin Kolb. “Conditional Survival Distributions of
    Brownian Trajectories in a One Dimensional Poissonian Environment in the Critical
    Case.” <i>Electronic Journal of Probability</i> 22 (2017). <a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>.
  ieee: 'M. Savov and M. Kolb, “Conditional survival distributions of Brownian trajectories
    in a one dimensional Poissonian environment in the critical case,” <i>Electronic
    Journal of Probability</i>, vol. 22, 2017, doi: <a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>.'
  mla: Savov, Mladen, and Martin Kolb. “Conditional Survival Distributions of Brownian
    Trajectories in a One Dimensional Poissonian Environment in the Critical Case.”
    <i>Electronic Journal of Probability</i>, vol. 22,  Institute of Mathematical
    Statistics &#38; Bernoulli Society, 2017, doi:<a href="https://doi.org/10.1214/17-EJP4468">https://doi.org/10.1214/17-EJP4468</a>.
  short: M. Savov, M. Kolb, Electronic Journal of Probability 22 (2017).
date_created: 2022-09-13T07:47:39Z
date_updated: 2022-09-13T07:47:46Z
department:
- _id: '96'
doi: https://doi.org/10.1214/17-EJP4468
intvolume: '        22'
language:
- iso: eng
publication: Electronic Journal of Probability
publication_status: published
publisher: ' Institute of Mathematical Statistics & Bernoulli Society'
status: public
title: Conditional survival distributions of Brownian trajectories in a one dimensional
  Poissonian environment in the critical case
type: journal_article
user_id: '85821'
volume: 22
year: '2017'
...
---
_id: '33343'
abstract:
- lang: eng
  text: "Using an operator-theoretic framework in a Hilbert-space setting, we perform
    a\r\ndetailed spectral analysis of the one-dimensional Laplacian in a bounded
    interval, subject to\r\nspecific non-self-adjoint connected boundary conditions
    modelling a random jump from the\r\nboundary to a point inside the interval. In
    accordance with previous works, we find that all the\r\neigenvalues are real.
    As the new results, we derive and analyse the adjoint operator, determine\r\nthe
    geometric and algebraic multiplicities of the eigenvalues, write down formulae
    for the\r\neigenfunctions together with the generalised eigenfunctions and study
    their basis properties.\r\nIt turns out that the latter heavily depend on whether
    the distance of the interior point to the\r\ncentre of the interval divided by
    the length of the interval is rational or irrational. Finally,\r\nwe find a closed
    formula for the metric operator that provides a similarity transform of the\r\nproblem
    to a self-adjoint operator."
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: David
  full_name: Krejčiřík, David
  last_name: Krejčiřík
citation:
  ama: Kolb M, Krejčiřík D. Spectral analysis of the diffusion operator with random
    jumps from the boundary. <i>Mathematische Zeitschrift</i>. 2016;284:877-900. doi:<a
    href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>
  apa: Kolb, M., &#38; Krejčiřík, D. (2016). Spectral analysis of the diffusion operator
    with random jumps from the boundary. <i>Mathematische Zeitschrift</i>, <i>284</i>,
    877–900. <a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>
  bibtex: '@article{Kolb_Krejčiřík_2016, title={Spectral analysis of the diffusion
    operator with random jumps from the boundary}, volume={284}, DOI={<a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>},
    journal={Mathematische Zeitschrift}, publisher={Springer}, author={Kolb, Martin
    and Krejčiřík, David}, year={2016}, pages={877–900} }'
  chicago: 'Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion
    Operator with Random Jumps from the Boundary.” <i>Mathematische Zeitschrift</i>
    284 (2016): 877–900. <a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.'
  ieee: 'M. Kolb and D. Krejčiřík, “Spectral analysis of the diffusion operator with
    random jumps from the boundary,” <i>Mathematische Zeitschrift</i>, vol. 284, pp.
    877–900, 2016, doi: <a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.'
  mla: Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion Operator
    with Random Jumps from the Boundary.” <i>Mathematische Zeitschrift</i>, vol. 284,
    Springer, 2016, pp. 877–900, doi:<a href="https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.
  short: M. Kolb, D. Krejčiřík, Mathematische Zeitschrift 284 (2016) 877–900.
date_created: 2022-09-13T07:56:56Z
date_updated: 2022-09-13T07:56:59Z
department:
- _id: '96'
doi: https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf
intvolume: '       284'
language:
- iso: eng
page: 877-900
publication: Mathematische Zeitschrift
publication_status: published
publisher: Springer
status: public
title: Spectral analysis of the diffusion operator with random jumps from the boundary
type: journal_article
user_id: '85821'
volume: 284
year: '2016'
...
---
_id: '33344'
abstract:
- lang: eng
  text: The hard disk model is a 2D Gibbsian process of particles interacting via
    pure hard core repulsion. At high particle density the model is believed to show
    orientational order, however, it is known not to exhibit positional order. Here
    we investigate to what extent particle positions may fluctuate. We consider a
    finite volume version of the model in a box of dimensions 2n ×  2n with arbitrary
    boundary configuration, and we show that the mean square displacement of particles
    near the center of the box is bounded from below by c log n. The result generalizes
    to a large class of models with fairly arbitrary interaction.
author:
- first_name: Thomas
  full_name: Richthammer, Thomas
  id: '62054'
  last_name: Richthammer
citation:
  ama: Richthammer T. Lower Bound on the Mean Square Displacement of Particles in
    the Hard Disk Model. <i>Communications in Mathematical Physics </i>. 2016;345:1077-1099.
    doi:<a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>
  apa: Richthammer, T. (2016). Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model. <i>Communications in Mathematical Physics </i>, <i>345</i>,
    1077–1099. <a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>
  bibtex: '@article{Richthammer_2016, title={Lower Bound on the Mean Square Displacement
    of Particles in the Hard Disk Model}, volume={345}, DOI={<a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>},
    journal={Communications in Mathematical Physics }, author={Richthammer, Thomas},
    year={2016}, pages={1077–1099} }'
  chicago: 'Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model.” <i>Communications in Mathematical Physics </i> 345 (2016):
    1077–99. <a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>.'
  ieee: 'T. Richthammer, “Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model,” <i>Communications in Mathematical Physics </i>, vol.
    345, pp. 1077–1099, 2016, doi: <a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>.'
  mla: Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles
    in the Hard Disk Model.” <i>Communications in Mathematical Physics </i>, vol.
    345, 2016, pp. 1077–99, doi:<a href="https://link.springer.com/article/10.1007/s00220-016-2584-0">https://link.springer.com/article/10.1007/s00220-016-2584-0</a>.
  short: T. Richthammer, Communications in Mathematical Physics  345 (2016) 1077–1099.
date_created: 2022-09-13T08:01:29Z
date_updated: 2022-09-13T08:01:36Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s00220-016-2584-0
intvolume: '       345'
language:
- iso: eng
page: 1077-1099
publication: 'Communications in Mathematical Physics '
publication_status: published
status: public
title: Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model
type: journal_article
user_id: '85821'
volume: 345
year: '2016'
...
---
_id: '33357'
abstract:
- lang: eng
  text: 'In this note we investigate the behaviour of Brownian motion conditioned
    on a growth constraint of its local time which has been previously investigated
    by Berestycki and Benjamini. For a class of non-decreasing positive functions
    f(t);t>0, we consider the Wiener measure under the condition that the Brownian
    local time is dominated by the function f up to time T. In the case where f(t)/t3/2
    is integrable we describe the limiting process as T goes to infinity. Moreover,
    we prove two conjectures in [BB10] in the case for a class of functions f, for
    which f(t)/t3/2 just fails to be integrable. Our methodology is more general as
    it relies on the study of the asymptotic of the probability of subordinators to
    stay above a given curve. Immediately or with adaptations one can study questions
    like the Brownian motioned conditioned on a growth constraint of its local time
    at the maximum or more generally a Levy process conditioned on a growth constraint
    of its local time at the maximum or at zero. We discuss briefly the former. '
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
citation:
  ama: Kolb M, Savov M. Transience and recurrence of a Brownian path with limited
    local time. <i>The Annals of Probability</i>. 2016;44(6). doi:<a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>
  apa: Kolb, M., &#38; Savov, M. (2016). Transience and recurrence of a Brownian path
    with limited local time. <i>The Annals of Probability</i>, <i>44</i>(6). <a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>
  bibtex: '@article{Kolb_Savov_2016, title={Transience and recurrence of a Brownian
    path with limited local time}, volume={44}, DOI={<a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>},
    number={6}, journal={The Annals of Probability}, publisher={Institute of Mathematical
    Statistics}, author={Kolb, Martin and Savov, Mladen}, year={2016} }'
  chicago: Kolb, Martin, and Mladen Savov. “Transience and Recurrence of a Brownian
    Path with Limited Local Time.” <i>The Annals of Probability</i> 44, no. 6 (2016).
    <a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>.
  ieee: 'M. Kolb and M. Savov, “Transience and recurrence of a Brownian path with
    limited local time,” <i>The Annals of Probability</i>, vol. 44, no. 6, 2016, doi:
    <a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>.'
  mla: Kolb, Martin, and Mladen Savov. “Transience and Recurrence of a Brownian Path
    with Limited Local Time.” <i>The Annals of Probability</i>, vol. 44, no. 6, Institute
    of Mathematical Statistics, 2016, doi:<a href="http://dx.doi.org/10.1214/15-AOP1069">http://dx.doi.org/10.1214/15-AOP1069</a>.
  short: M. Kolb, M. Savov, The Annals of Probability 44 (2016).
date_created: 2022-09-14T04:22:23Z
date_updated: 2022-09-14T04:22:26Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/15-AOP1069
intvolume: '        44'
issue: '6'
language:
- iso: eng
publication: The Annals of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Transience and recurrence of a Brownian path with limited local time
type: journal_article
user_id: '85821'
volume: 44
year: '2016'
...
---
_id: '33359'
abstract:
- lang: eng
  text: 'We consider Gibbs distributions on permutations of a locally finite infinite
    set X⊂R, where a permutation σ of X is assigned (formal) energy ∑x∈XV(σ(x)−x).
    This is motivated by Feynman’s path representation of the quantum Bose gas; the
    choice X:=Z and V(x):=αx2 is of principal interest. Under suitable regularity
    conditions on the set X and the potential V, we establish existence and a full
    classification of the infinite-volume Gibbs measures for this problem, including
    a result on the number of infinite cycles of typical permutations. Unlike earlier
    results, our conclusions are not limited to small densities and/or high temperatures. '
author:
- first_name: Thomas
  full_name: Richthammer, Thomas
  id: '62054'
  last_name: Richthammer
- first_name: Marek
  full_name: Biskup, Marek
  last_name: Biskup
citation:
  ama: Richthammer T, Biskup M. Gibbs measures on permutations over one-dimensional
    discrete point sets. <i>Communications in Mathematical Physics</i>. 2015;25(2):898-929.
    doi:<a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>
  apa: Richthammer, T., &#38; Biskup, M. (2015). Gibbs measures on permutations over
    one-dimensional discrete point sets. <i>Communications in Mathematical Physics</i>,
    <i>25</i>(2), 898–929. <a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>
  bibtex: '@article{Richthammer_Biskup_2015, title={Gibbs measures on permutations
    over one-dimensional discrete point sets}, volume={25}, DOI={<a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>},
    number={2}, journal={Communications in Mathematical Physics}, publisher={Springer
    Science+Business Media}, author={Richthammer, Thomas and Biskup, Marek}, year={2015},
    pages={898–929} }'
  chicago: 'Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations
    over One-Dimensional Discrete Point Sets.” <i>Communications in Mathematical Physics</i>
    25, no. 2 (2015): 898–929. <a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>.'
  ieee: 'T. Richthammer and M. Biskup, “Gibbs measures on permutations over one-dimensional
    discrete point sets,” <i>Communications in Mathematical Physics</i>, vol. 25,
    no. 2, pp. 898–929, 2015, doi: <a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>.'
  mla: Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over
    One-Dimensional Discrete Point Sets.” <i>Communications in Mathematical Physics</i>,
    vol. 25, no. 2, Springer Science+Business Media, 2015, pp. 898–929, doi:<a href="https://doi.org/10.48550/arXiv.1310.0248">https://doi.org/10.48550/arXiv.1310.0248</a>.
  short: T. Richthammer, M. Biskup, Communications in Mathematical Physics 25 (2015)
    898–929.
date_created: 2022-09-14T04:57:58Z
date_updated: 2022-09-14T04:58:02Z
department:
- _id: '96'
doi: https://doi.org/10.48550/arXiv.1310.0248
intvolume: '        25'
issue: '2'
language:
- iso: eng
page: 898-929
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer Science+Business Media
status: public
title: Gibbs measures on permutations over one-dimensional discrete point sets
type: journal_article
user_id: '85821'
volume: 25
year: '2015'
...
---
_id: '33358'
abstract:
- lang: eng
  text: 'We study the workload processes of two M/G/1 queueing systems with restricted
    capacity: in Model 1 any service requirement that would exceed a certain capacity
    threshold is truncated; in Model 2 new arrivals do not enter the system if they
    have to wait more than a fixed threshold time in line. For Model 1 we obtain several
    results concerning the rate of convergence to equilibrium. In particular, we derive
    uniform bounds for geometric ergodicity with respect to certain subclasses. For
    Model 2 geometric ergodicity follows from the finiteness of the moment-generating
    function of the service time distribution. We derive bounds for the convergence
    rates in special cases. The proofs use the coupling method.'
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Wolfgang
  full_name: Stadje, Wolfgang
  last_name: Stadje
- first_name: Achim
  full_name: Wübker, Achim
  last_name: Wübker
citation:
  ama: Kolb M, Stadje W, Wübker A. The rate of convergence to stationarity for M/G/1
    models with admission controls via coupling. <i>Stochastic Models</i>. 2015;32(1):121-135.
    doi:<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>
  apa: Kolb, M., Stadje, W., &#38; Wübker, A. (2015). The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling. <i>Stochastic Models</i>,
    <i>32</i>(1), 121–135. <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>
  bibtex: '@article{Kolb_Stadje_Wübker_2015, title={The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling}, volume={32}, DOI={<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>},
    number={1}, journal={Stochastic Models}, publisher={INFORMS}, author={Kolb, Martin
    and Stadje, Wolfgang and Wübker, Achim}, year={2015}, pages={121–135} }'
  chicago: 'Kolb, Martin, Wolfgang Stadje, and Achim Wübker. “The Rate of Convergence
    to Stationarity for M/G/1 Models with Admission Controls via Coupling.” <i>Stochastic
    Models</i> 32, no. 1 (2015): 121–35. <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.'
  ieee: 'M. Kolb, W. Stadje, and A. Wübker, “The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling,” <i>Stochastic Models</i>,
    vol. 32, no. 1, pp. 121–135, 2015, doi: <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.'
  mla: Kolb, Martin, et al. “The Rate of Convergence to Stationarity for M/G/1 Models
    with Admission Controls via Coupling.” <i>Stochastic Models</i>, vol. 32, no.
    1, INFORMS, 2015, pp. 121–35, doi:<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.
  short: M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.
date_created: 2022-09-14T04:52:15Z
date_updated: 2022-09-14T04:52:19Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1080/15326349.2015.1090322
intvolume: '        32'
issue: '1'
language:
- iso: eng
page: 121-135
publication: Stochastic Models
publication_status: published
publisher: INFORMS
status: public
title: The rate of convergence to stationarity for M/G/1 models with admission controls
  via coupling
type: journal_article
user_id: '85821'
volume: 32
year: '2015'
...
---
_id: '33360'
abstract:
- lang: eng
  text: We prove a local limit theorem for the area of the positive excursion of random
    walks with zero mean and finite variance. Our main result complements previous
    work of Caravenna and Chaumont; Sohier, as well as Kim and Pittel.
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Denis
  full_name: Denisov, Denis
  last_name: Denisov
- first_name: Vitali
  full_name: Wachtel, Vitali
  last_name: Wachtel
citation:
  ama: Kolb M, Denisov D, Wachtel V. Local asymptotics for the area of random walk
    excursions. <i>Journal of the London Mathematical Society</i>. 2015;91(2):495-513.
  apa: Kolb, M., Denisov, D., &#38; Wachtel, V. (2015). Local asymptotics for the
    area of random walk excursions. <i>Journal of the London Mathematical Society</i>,
    <i>91</i>(2), 495–513.
  bibtex: '@article{Kolb_Denisov_Wachtel_2015, title={Local asymptotics for the area
    of random walk excursions}, volume={91}, number={2}, journal={Journal of the London
    Mathematical Society}, publisher={London Mathematical Society}, author={Kolb,
    Martin and Denisov, Denis and Wachtel, Vitali}, year={2015}, pages={495–513} }'
  chicago: 'Kolb, Martin, Denis Denisov, and Vitali Wachtel. “Local Asymptotics for
    the Area of Random Walk Excursions.” <i>Journal of the London Mathematical Society</i>
    91, no. 2 (2015): 495–513.'
  ieee: M. Kolb, D. Denisov, and V. Wachtel, “Local asymptotics for the area of random
    walk excursions,” <i>Journal of the London Mathematical Society</i>, vol. 91,
    no. 2, pp. 495–513, 2015.
  mla: Kolb, Martin, et al. “Local Asymptotics for the Area of Random Walk Excursions.”
    <i>Journal of the London Mathematical Society</i>, vol. 91, no. 2, London Mathematical
    Society, 2015, pp. 495–513.
  short: M. Kolb, D. Denisov, V. Wachtel, Journal of the London Mathematical Society
    91 (2015) 495–513.
date_created: 2022-09-14T05:01:41Z
date_updated: 2022-09-14T05:01:45Z
department:
- _id: '96'
intvolume: '        91'
issue: '2'
language:
- iso: eng
page: 495-513
publication: Journal of the London Mathematical Society
publication_status: published
publisher: London Mathematical Society
status: public
title: Local asymptotics for the area of random walk excursions
type: journal_article
user_id: '85821'
volume: 91
year: '2015'
...
---
_id: '33361'
abstract:
- lang: eng
  text: Following Bertoin who considered the ergodicity and exponential decay of Lévy
    processes in a finite domain, we consider general Lévy processes and their ergodicity
    and exponential decay in a finite interval. More precisely, given Ta=inf{t>0:Xt∉.
    Under general conditions, e.g. absolute continuity of the transition semigroup
    of the unkilled Lévy process, we prove that the killed semigroup is a compact
    operator. Thus, we prove stronger results in view of the exponential ergodicity
    and estimates of the speed of convergence. Our results are presented in a Lévy
    processes setting but are well applicable for Markov processes in a finite interval
    under information about Lebesgue irreducibility of the killed semigroup and that
    the killed process is a double Feller process. For example, this scheme is applicable
    to a work of Pistorius.<br />
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
citation:
  ama: Kolb M, Savov M. Exponential ergodicity of killed Lévy processes in a finite
    interval. <i>Electronic Communications in Probability</i>. 2014;19(31):1-9. doi:<a
    href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>
  apa: Kolb, M., &#38; Savov, M. (2014). Exponential ergodicity of killed Lévy processes
    in a finite interval. <i>Electronic Communications in Probability</i>, <i>19</i>(31),
    1–9. <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>
  bibtex: '@article{Kolb_Savov_2014, title={Exponential ergodicity of killed Lévy
    processes in a finite interval}, volume={19}, DOI={<a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>},
    number={31}, journal={Electronic Communications in Probability}, publisher={Institute
    of Mathematical Statistics (IMS)}, author={Kolb, Martin and Savov, Mladen}, year={2014},
    pages={1–9} }'
  chicago: 'Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy
    Processes in a Finite Interval.” <i>Electronic Communications in Probability</i>
    19, no. 31 (2014): 1–9. <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.'
  ieee: 'M. Kolb and M. Savov, “Exponential ergodicity of killed Lévy processes in
    a finite interval,” <i>Electronic Communications in Probability</i>, vol. 19,
    no. 31, pp. 1–9, 2014, doi: <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.'
  mla: Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy Processes
    in a Finite Interval.” <i>Electronic Communications in Probability</i>, vol. 19,
    no. 31, Institute of Mathematical Statistics (IMS), 2014, pp. 1–9, doi:<a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.
  short: M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9.
date_created: 2022-09-14T05:15:00Z
date_updated: 2022-09-14T05:15:06Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/ECP.v19-3006
intvolume: '        19'
issue: '31'
language:
- iso: eng
page: 1-9
publication: Electronic Communications in Probability
publication_status: published
publisher: Institute of Mathematical Statistics (IMS)
status: public
title: Exponential ergodicity of killed Lévy processes in a finite interval
type: journal_article
user_id: '85821'
volume: 19
year: '2014'
...
---
_id: '33362'
abstract:
- lang: eng
  text: We study the influence of the intrinsic curvature on the large time behaviour
    of the heat equation in a tubular neighbourhood of an unbounded geodesic in a
    two-dimensional Riemannian manifold. Since we consider killing boundary conditions,
    there is always an exponential-type decay for the heat semigroup. We show that
    this exponential-type decay is slower for positively curved manifolds comparing
    to the flat case. As the main result, we establish a sharp extra polynomial-type
    decay for the heat semigroup on negatively curved manifolds comparing to the flat
    case. The proof employs the existence of Hardy-type inequalities for the Dirichlet
    Laplacian in the tubular neighbourhoods on negatively curved manifolds and the
    method of self-similar variables and weighted Sobolev spaces for the heat equation.
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: David
  full_name: Krejčiřík, David
  last_name: Krejčiřík
citation:
  ama: Kolb M, Krejčiřík D. The Brownian traveller on manifolds. <i>Journal of Spectral
    Theory</i>. 2014;4(2):235-281. doi:<a href="https://doi.org/10.4171/jst/69">https://doi.org/10.4171/jst/69</a>
  apa: Kolb, M., &#38; Krejčiřík, D. (2014). The Brownian traveller on manifolds.
    <i>Journal of Spectral Theory</i>, <i>4</i>(2), 235–281. <a href="https://doi.org/10.4171/jst/69">https://doi.org/10.4171/jst/69</a>
  bibtex: '@article{Kolb_Krejčiřík_2014, title={The Brownian traveller on manifolds},
    volume={4}, DOI={<a href="https://doi.org/10.4171/jst/69">https://doi.org/10.4171/jst/69</a>},
    number={2}, journal={Journal of Spectral Theory}, publisher={EMS Press}, author={Kolb,
    Martin and Krejčiřík, David}, year={2014}, pages={235–281} }'
  chicago: 'Kolb, Martin, and David Krejčiřík. “The Brownian Traveller on Manifolds.”
    <i>Journal of Spectral Theory</i> 4, no. 2 (2014): 235–81. <a href="https://doi.org/10.4171/jst/69">https://doi.org/10.4171/jst/69</a>.'
  ieee: 'M. Kolb and D. Krejčiřík, “The Brownian traveller on manifolds,” <i>Journal
    of Spectral Theory</i>, vol. 4, no. 2, pp. 235–281, 2014, doi: <a href="https://doi.org/10.4171/jst/69">https://doi.org/10.4171/jst/69</a>.'
  mla: Kolb, Martin, and David Krejčiřík. “The Brownian Traveller on Manifolds.” <i>Journal
    of Spectral Theory</i>, vol. 4, no. 2, EMS Press, 2014, pp. 235–81, doi:<a href="https://doi.org/10.4171/jst/69">https://doi.org/10.4171/jst/69</a>.
  short: M. Kolb, D. Krejčiřík, Journal of Spectral Theory 4 (2014) 235–281.
date_created: 2022-09-14T05:18:39Z
date_updated: 2022-09-14T05:18:42Z
department:
- _id: '96'
doi: https://doi.org/10.4171/jst/69
intvolume: '         4'
issue: '2'
language:
- iso: eng
page: 235-281
publication: Journal of Spectral Theory
publication_status: published
publisher: EMS Press
status: public
title: The Brownian traveller on manifolds
type: journal_article
user_id: '85821'
volume: 4
year: '2014'
...
---
_id: '37503'
abstract:
- lang: eng
  text: 'This paper extends and clarifies results of Steinsaltz and Evans [Trans.
    Amer. Math. Soc. 359 (2007) 1285–1234], which found conditions for convergence
    of a killed one-dimensional diffusion conditioned on survival, to a quasistationary
    distribution whose density is given by the principal eigenfunction of the generator.
    Under the assumption that the limit of the killing at infinity differs from the
    principal eigenvalue we prove that convergence to quasistationarity occurs if
    and only if the principal eigenfunction is integrable. When the killing at ∞ is
    larger than the principal eigenvalue, then the eigenfunction is always integrable.
    When the killing at ∞ is smaller, the eigenfunction is integrable only when the
    unkilled process is recurrent; otherwise, the process conditioned on survival
    converges to 0 density on any bounded interval. '
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: David
  full_name: Steinsaltz, David
  last_name: Steinsaltz
citation:
  ama: Kolb M, Steinsaltz D. Quasilimiting behavior for one-dimensional diffusions
    with killing. <i>Annals of Probability</i>. 2012;40(1):162-212. doi:<a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>
  apa: Kolb, M., &#38; Steinsaltz, D. (2012). Quasilimiting behavior for one-dimensional
    diffusions with killing. <i>Annals of Probability</i>, <i>40</i>(1), 162–212.
    <a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>
  bibtex: '@article{Kolb_Steinsaltz_2012, title={Quasilimiting behavior for one-dimensional
    diffusions with killing}, volume={40}, DOI={<a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>},
    number={1}, journal={Annals of Probability}, publisher={Institute of Mathematical
    Statistics}, author={Kolb, Martin and Steinsaltz, David}, year={2012}, pages={162–212}
    }'
  chicago: 'Kolb, Martin, and David Steinsaltz. “Quasilimiting Behavior for One-Dimensional
    Diffusions with Killing.” <i>Annals of Probability</i> 40, no. 1 (2012): 162–212.
    <a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>.'
  ieee: 'M. Kolb and D. Steinsaltz, “Quasilimiting behavior for one-dimensional diffusions
    with killing,” <i>Annals of Probability</i>, vol. 40, no. 1, pp. 162–212, 2012,
    doi: <a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>.'
  mla: Kolb, Martin, and David Steinsaltz. “Quasilimiting Behavior for One-Dimensional
    Diffusions with Killing.” <i>Annals of Probability</i>, vol. 40, no. 1, Institute
    of Mathematical Statistics, 2012, pp. 162–212, doi:<a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>.
  short: M. Kolb, D. Steinsaltz, Annals of Probability 40 (2012) 162–212.
date_created: 2023-01-19T06:55:03Z
date_updated: 2023-01-19T06:55:09Z
department:
- _id: '96'
doi: https://doi.org/10.1214/10-AOP623
intvolume: '        40'
issue: '1'
language:
- iso: eng
page: 162-212
publication: Annals of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Quasilimiting behavior for one-dimensional diffusions with killing
type: journal_article
user_id: '85821'
volume: 40
year: '2012'
...
---
_id: '45765'
author:
- first_name: Robert
  full_name: Grummt, Robert
  last_name: Grummt
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Grummt R, Kolb M. Essential selfadjointness of singular magnetic Schrödinger
    operators on Riemannian manifolds. <i> Journal of Mathematical Analysis and Applications</i>.
    2012;388:480-489. doi:<a href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>
  apa: Grummt, R., &#38; Kolb, M. (2012). Essential selfadjointness of singular magnetic
    Schrödinger operators on Riemannian manifolds. <i> Journal of Mathematical Analysis
    and Applications</i>, <i>388</i>, 480–489. <a href="https://doi.org/10.1016/j.jmaa.2011.09.060">https://doi.org/10.1016/j.jmaa.2011.09.060</a>
  bibtex: '@article{Grummt_Kolb_2012, title={Essential selfadjointness of singular
    magnetic Schrödinger operators on Riemannian manifolds}, volume={388}, DOI={<a
    href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>},
    journal={ Journal of Mathematical Analysis and Applications}, author={Grummt,
    Robert and Kolb, Martin}, year={2012}, pages={480–489} }'
  chicago: 'Grummt, Robert, and Martin Kolb. “Essential Selfadjointness of Singular
    Magnetic Schrödinger Operators on Riemannian Manifolds.” <i> Journal of Mathematical
    Analysis and Applications</i> 388 (2012): 480–89. <a href="https://doi.org/10.1016/j.jmaa.2011.09.060">https://doi.org/10.1016/j.jmaa.2011.09.060</a>.'
  ieee: 'R. Grummt and M. Kolb, “Essential selfadjointness of singular magnetic Schrödinger
    operators on Riemannian manifolds,” <i> Journal of Mathematical Analysis and Applications</i>,
    vol. 388, pp. 480–489, 2012, doi: <a href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>.'
  mla: Grummt, Robert, and Martin Kolb. “Essential Selfadjointness of Singular Magnetic
    Schrödinger Operators on Riemannian Manifolds.” <i> Journal of Mathematical Analysis
    and Applications</i>, vol. 388, 2012, pp. 480–89, doi:<a href="https://doi.org/10.1016/j.jmaa.2011.09.060">10.1016/j.jmaa.2011.09.060</a>.
  short: R. Grummt, M. Kolb,  Journal of Mathematical Analysis and Applications 388
    (2012) 480–489.
date_created: 2023-06-26T08:04:27Z
date_updated: 2023-06-26T08:04:47Z
department:
- _id: '96'
doi: 10.1016/j.jmaa.2011.09.060
intvolume: '       388'
language:
- iso: eng
page: 480-489
publication: ' Journal of Mathematical Analysis and Applications'
status: public
title: Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian
  manifolds
type: journal_article
user_id: '14931'
volume: 388
year: '2012'
...
---
_id: '37500'
abstract:
- lang: eng
  text: 'We discuss the time evolution of the wave function which is the solution
    of a stochastic Schrödinger equation describing the dynamics of a free quantum
    particle subject to spontaneous localizations in space. We prove global existence
    and uniqueness of solutions. We observe that there exist three time regimes: the
    collapse regime, the classical regime and the diffusive regime. Concerning the
    latter, we assert that the general solution converges almost surely to a diffusing
    Gaussian wave function having a finite spread both in position as well as in momentum.
    This paper corrects and completes earlier works on this issue.'
author:
- first_name: Angelo
  full_name: Bassi, Angelo
  last_name: Bassi
- first_name: Detlef
  full_name: Dürr, Detlef
  last_name: Dürr
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
citation:
  ama: Bassi A, Dürr D, Kolb M. ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER
    EVOLUTIONS. <i>Reviews in Mathematical Physics</i>. 2009;22(1):55-89. doi:<a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>
  apa: Bassi, A., Dürr, D., &#38; Kolb, M. (2009). ON THE LONG TIME BEHAVIOR OF FREE
    STOCHASTIC SCHRÖDINGER EVOLUTIONS. <i>Reviews in Mathematical Physics</i>, <i>22</i>(1),
    55–89. <a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>
  bibtex: '@article{Bassi_Dürr_Kolb_2009, title={ON THE LONG TIME BEHAVIOR OF FREE
    STOCHASTIC SCHRÖDINGER EVOLUTIONS}, volume={22}, DOI={<a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>},
    number={1}, journal={Reviews in Mathematical Physics}, author={Bassi, Angelo and
    Dürr, Detlef and Kolb, Martin}, year={2009}, pages={55–89} }'
  chicago: 'Bassi, Angelo, Detlef Dürr, and Martin Kolb. “ON THE LONG TIME BEHAVIOR
    OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” <i>Reviews in Mathematical Physics</i>
    22, no. 1 (2009): 55–89. <a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>.'
  ieee: 'A. Bassi, D. Dürr, and M. Kolb, “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC
    SCHRÖDINGER EVOLUTIONS,” <i>Reviews in Mathematical Physics</i>, vol. 22, no.
    1, pp. 55–89, 2009, doi: <a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>.'
  mla: Bassi, Angelo, et al. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER
    EVOLUTIONS.” <i>Reviews in Mathematical Physics</i>, vol. 22, no. 1, 2009, pp.
    55–89, doi:<a href="https://doi.org/10.1142/S0129055X10003886">https://doi.org/10.1142/S0129055X10003886</a>.
  short: A. Bassi, D. Dürr, M. Kolb, Reviews in Mathematical Physics 22 (2009) 55–89.
date_created: 2023-01-19T06:49:37Z
date_updated: 2023-01-19T06:49:46Z
department:
- _id: '96'
doi: https://doi.org/10.1142/S0129055X10003886
intvolume: '        22'
issue: '1'
language:
- iso: eng
page: 55-89
publication: Reviews in Mathematical Physics
publication_status: published
status: public
title: ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS
type: journal_article
user_id: '85821'
volume: 22
year: '2009'
...