[{"year":"2019","citation":{"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} }","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).","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>.","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>"},"intvolume":"        29","issue":"1","title":"Theoretical properties of quasi-stationary Monte Carlo methods","doi":"http://dx.doi.org/10.1214/18-AAP1422","date_updated":"2022-09-12T07:32:35Z","date_created":"2022-09-12T07:24:52Z","author":[{"last_name":"Wang","full_name":"Wang, Andi Q.","first_name":"Andi Q."},{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"},{"first_name":"Gareth O.","full_name":"Roberts, Gareth O.","last_name":"Roberts"},{"first_name":"David","full_name":"Steinsaltz, David","last_name":"Steinsaltz"}],"volume":29,"status":"public","type":"journal_article","publication":"The Annals of Applied Probability","language":[{"iso":"eng"}],"_id":"33333","user_id":"85821","department":[{"_id":"96"}]},{"department":[{"_id":"96"}],"user_id":"85821","_id":"33334","language":[{"iso":"eng"}],"publication":"Stochastic Processes and their Applications","type":"journal_article","status":"public","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)."}],"volume":129,"author":[{"full_name":"Hening, Alexandru","last_name":"Hening","first_name":"Alexandru"},{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb"}],"date_created":"2022-09-12T07:46:44Z","publisher":"Bernoulli Society for Mathematical Statistics and Probability","date_updated":"2022-09-12T07:46:47Z","doi":"http://dx.doi.org/10.1016/j.spa.2018.05.012","title":"Quasistationary distributions for one-dimensional diffusions with two singular boundary points","issue":"5","publication_status":"published","page":"1659-1696","intvolume":"       129","citation":{"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>","short":"A. Hening, M. Kolb, Stochastic Processes and Their Applications 129 (2019) 1659–1696.","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>.","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>.","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>"},"year":"2019"},{"year":"2018","intvolume":"        33","page":"65–102","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>","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>.","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>.","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>","short":"G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018) 65–102.","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} }","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>."},"publication_status":"published","title":"Persistence of one-dimensional AR(1)-processes","doi":"https://link.springer.com/article/10.1007/s10959-018-0850-0","publisher":"Springer Science + Business Media","date_updated":"2022-09-12T07:52:44Z","volume":33,"date_created":"2022-09-12T07:50:38Z","author":[{"first_name":"Günter","full_name":"Hinrichs, Günter","last_name":"Hinrichs"},{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Vitali","full_name":"Wachtel, Vitali","last_name":"Wachtel"}],"abstract":[{"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.","lang":"eng"}],"status":"public","publication":"Journal of Theoretical Probability","type":"journal_article","language":[{"iso":"eng"}],"_id":"33335","department":[{"_id":"96"}],"user_id":"85821"},{"type":"journal_article","publication":"Letters in Mathematical Physics","abstract":[{"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.","lang":"eng"}],"status":"public","_id":"33336","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}],"publication_status":"published","year":"2017","citation":{"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} }","short":"L. Boßmann, R. Grummt, M. Kolb, Letters in Mathematical Physics 108 (2017) 185–193.","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>.","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>","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>","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>.","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>."},"intvolume":"       108","page":"185–193","date_updated":"2022-09-12T08:08:09Z","author":[{"first_name":"Lea","full_name":"Boßmann, Lea","last_name":"Boßmann"},{"first_name":"Robert","full_name":"Grummt, Robert","last_name":"Grummt"},{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"}],"date_created":"2022-09-12T08:08:05Z","volume":108,"title":"On the dipole approximation with error estimates","doi":"https://link.springer.com/article/10.1007/s11005-017-0999-y"},{"_id":"33342","department":[{"_id":"96"}],"user_id":"85821","language":[{"iso":"eng"}],"publication":"Electronic Journal of Probability","type":"journal_article","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]."}],"status":"public","publisher":" Institute of Mathematical Statistics & Bernoulli Society","date_updated":"2022-09-13T07:47:46Z","volume":22,"date_created":"2022-09-13T07:47:39Z","author":[{"first_name":"Mladen","last_name":"Savov","full_name":"Savov, Mladen"},{"first_name":"Martin","id":"48880","full_name":"Kolb, Martin","last_name":"Kolb"}],"title":"Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case","doi":"https://doi.org/10.1214/17-EJP4468","publication_status":"published","year":"2017","intvolume":"        22","citation":{"short":"M. Savov, M. Kolb, Electronic Journal of Probability 22 (2017).","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>.","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} }","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>","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>.","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>"}},{"type":"journal_article","publication":"Mathematische Zeitschrift","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."}],"status":"public","_id":"33343","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}],"publication_status":"published","year":"2016","citation":{"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>","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>.","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} }","short":"M. Kolb, D. Krejčiřík, Mathematische Zeitschrift 284 (2016) 877–900.","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>.","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>.","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>"},"page":"877-900","intvolume":"       284","date_updated":"2022-09-13T07:56:59Z","publisher":"Springer","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"first_name":"David","full_name":"Krejčiřík, David","last_name":"Krejčiřík"}],"date_created":"2022-09-13T07:56:56Z","volume":284,"title":"Spectral analysis of the diffusion operator with random jumps from the boundary","doi":"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf"},{"title":"Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model","doi":"https://link.springer.com/article/10.1007/s00220-016-2584-0","date_updated":"2022-09-13T08:01:36Z","volume":345,"author":[{"first_name":"Thomas","full_name":"Richthammer, Thomas","id":"62054","last_name":"Richthammer"}],"date_created":"2022-09-13T08:01:29Z","year":"2016","page":"1077-1099","intvolume":"       345","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>","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>.","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>","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.","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} }"},"publication_status":"published","language":[{"iso":"eng"}],"_id":"33344","department":[{"_id":"96"}],"user_id":"85821","abstract":[{"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.","lang":"eng"}],"status":"public","publication":"Communications in Mathematical Physics ","type":"journal_article"},{"_id":"33357","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"The Annals of Probability","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. "}],"status":"public","publisher":"Institute of Mathematical Statistics","date_updated":"2022-09-14T04:22:26Z","author":[{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"date_created":"2022-09-14T04:22:23Z","volume":44,"title":"Transience and recurrence of a Brownian path with limited local time","doi":"http://dx.doi.org/10.1214/15-AOP1069","publication_status":"published","issue":"6","year":"2016","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>","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).","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} }","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>"},"intvolume":"        44"},{"volume":25,"date_created":"2022-09-14T04:57:58Z","author":[{"first_name":"Thomas","id":"62054","full_name":"Richthammer, Thomas","last_name":"Richthammer"},{"full_name":"Biskup, Marek","last_name":"Biskup","first_name":"Marek"}],"publisher":"Springer Science+Business Media","date_updated":"2022-09-14T04:58:02Z","doi":"https://doi.org/10.48550/arXiv.1310.0248","title":"Gibbs measures on permutations over one-dimensional discrete point sets","issue":"2","publication_status":"published","intvolume":"        25","page":"898-929","citation":{"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} }","short":"T. Richthammer, M. Biskup, Communications in Mathematical Physics 25 (2015) 898–929.","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>.","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>","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>","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>.","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>."},"year":"2015","department":[{"_id":"96"}],"user_id":"85821","_id":"33359","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","type":"journal_article","status":"public","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. "}]},{"title":"The rate of convergence to stationarity for M/G/1 models with admission controls via coupling","doi":"http://dx.doi.org/10.1080/15326349.2015.1090322","date_updated":"2022-09-14T04:52:19Z","publisher":"INFORMS","author":[{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"},{"full_name":"Stadje, Wolfgang","last_name":"Stadje","first_name":"Wolfgang"},{"first_name":"Achim","last_name":"Wübker","full_name":"Wübker, Achim"}],"date_created":"2022-09-14T04:52:15Z","volume":32,"year":"2015","citation":{"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>","short":"M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.","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} }","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>.","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>","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>.","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>."},"page":"121-135","intvolume":"        32","publication_status":"published","issue":"1","language":[{"iso":"eng"}],"_id":"33358","user_id":"85821","department":[{"_id":"96"}],"abstract":[{"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.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Stochastic Models"},{"type":"journal_article","publication":"Journal of the London Mathematical Society","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."}],"status":"public","_id":"33360","user_id":"85821","department":[{"_id":"96"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"2","year":"2015","citation":{"short":"M. Kolb, D. Denisov, V. Wachtel, Journal of the London Mathematical Society 91 (2015) 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} }","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.","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.","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.","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."},"page":"495-513","intvolume":"        91","date_updated":"2022-09-14T05:01:45Z","publisher":"London Mathematical Society","author":[{"first_name":"Martin","last_name":"Kolb","id":"48880","full_name":"Kolb, Martin"},{"last_name":"Denisov","full_name":"Denisov, Denis","first_name":"Denis"},{"first_name":"Vitali","last_name":"Wachtel","full_name":"Wachtel, Vitali"}],"date_created":"2022-09-14T05:01:41Z","volume":91,"title":"Local asymptotics for the area of random walk excursions"},{"year":"2014","citation":{"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} }","short":"M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9.","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>.","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>","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>.","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>"},"page":"1-9","intvolume":"        19","publication_status":"published","issue":"31","title":"Exponential ergodicity of killed Lévy processes in a finite interval","doi":"http://dx.doi.org/10.1214/ECP.v19-3006","publisher":"Institute of Mathematical Statistics (IMS)","date_updated":"2022-09-14T05:15:06Z","date_created":"2022-09-14T05:15:00Z","author":[{"id":"48880","full_name":"Kolb, Martin","last_name":"Kolb","first_name":"Martin"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"volume":19,"abstract":[{"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 />","lang":"eng"}],"status":"public","type":"journal_article","publication":"Electronic Communications in Probability","language":[{"iso":"eng"}],"_id":"33361","user_id":"85821","department":[{"_id":"96"}]},{"publication":"Journal of Spectral Theory","type":"journal_article","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."}],"status":"public","_id":"33362","department":[{"_id":"96"}],"user_id":"85821","language":[{"iso":"eng"}],"publication_status":"published","issue":"2","year":"2014","intvolume":"         4","page":"235-281","citation":{"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>.","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>","short":"M. Kolb, D. Krejčiřík, Journal of Spectral Theory 4 (2014) 235–281.","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>.","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} }"},"publisher":"EMS Press","date_updated":"2022-09-14T05:18:42Z","volume":4,"author":[{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"},{"first_name":"David","last_name":"Krejčiřík","full_name":"Krejčiřík, David"}],"date_created":"2022-09-14T05:18:39Z","title":"The Brownian traveller on manifolds","doi":"https://doi.org/10.4171/jst/69"},{"_id":"37503","department":[{"_id":"96"}],"user_id":"85821","language":[{"iso":"eng"}],"publication":"Annals of Probability","type":"journal_article","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. "}],"status":"public","date_updated":"2023-01-19T06:55:09Z","publisher":"Institute of Mathematical Statistics","volume":40,"date_created":"2023-01-19T06:55:03Z","author":[{"first_name":"Martin","last_name":"Kolb","id":"48880","full_name":"Kolb, Martin"},{"last_name":"Steinsaltz","full_name":"Steinsaltz, David","first_name":"David"}],"title":"Quasilimiting behavior for one-dimensional diffusions with killing","doi":"https://doi.org/10.1214/10-AOP623","publication_status":"published","issue":"1","year":"2012","page":"162-212","intvolume":"        40","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>","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>.","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>","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>.","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} }","short":"M. Kolb, D. Steinsaltz, Annals of Probability 40 (2012) 162–212."}},{"status":"public","publication":" Journal of Mathematical Analysis and Applications","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"96"}],"user_id":"14931","_id":"45765","page":"480-489","intvolume":"       388","citation":{"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>","short":"R. Grummt, M. Kolb,  Journal of Mathematical Analysis and Applications 388 (2012) 480–489.","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} }","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>.","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>","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>."},"year":"2012","doi":"10.1016/j.jmaa.2011.09.060","title":"Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds","volume":388,"author":[{"first_name":"Robert","last_name":"Grummt","full_name":"Grummt, Robert"},{"full_name":"Kolb, Martin","id":"48880","last_name":"Kolb","first_name":"Martin"}],"date_created":"2023-06-26T08:04:27Z","date_updated":"2023-06-26T08:04:47Z"},{"issue":"1","publication_status":"published","citation":{"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>.","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>.","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>","short":"A. Bassi, D. Dürr, M. Kolb, Reviews in Mathematical Physics 22 (2009) 55–89.","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>.","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} }","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>"},"page":"55-89","intvolume":"        22","year":"2009","author":[{"full_name":"Bassi, Angelo","last_name":"Bassi","first_name":"Angelo"},{"first_name":"Detlef","full_name":"Dürr, Detlef","last_name":"Dürr"},{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"}],"date_created":"2023-01-19T06:49:37Z","volume":22,"date_updated":"2023-01-19T06:49:46Z","doi":"https://doi.org/10.1142/S0129055X10003886","title":"ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS","type":"journal_article","publication":"Reviews in Mathematical Physics","status":"public","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."}],"user_id":"85821","department":[{"_id":"96"}],"_id":"37500","language":[{"iso":"eng"}]}]