---
_id: '66641'
article_number: '104996'
author:
- first_name: Jonas
  full_name: Jalowy, Jonas
  id: '113768'
  last_name: Jalowy
  orcid: 0000-0001-9624-2685
- first_name: Hanna
  full_name: Stange, Hanna
  last_name: Stange
citation:
  ama: Jalowy J, Stange H. Box-covariances of hyperuniform point processes. <i>Stochastic
    Processes and their Applications</i>. 2026;199. doi:<a href="https://doi.org/10.1016/j.spa.2026.104996">10.1016/j.spa.2026.104996</a>
  apa: Jalowy, J., &#38; Stange, H. (2026). Box-covariances of hyperuniform point
    processes. <i>Stochastic Processes and Their Applications</i>, <i>199</i>, Article
    104996. <a href="https://doi.org/10.1016/j.spa.2026.104996">https://doi.org/10.1016/j.spa.2026.104996</a>
  bibtex: '@article{Jalowy_Stange_2026, title={Box-covariances of hyperuniform point
    processes}, volume={199}, DOI={<a href="https://doi.org/10.1016/j.spa.2026.104996">10.1016/j.spa.2026.104996</a>},
    number={104996}, journal={Stochastic Processes and their Applications}, publisher={Elsevier
    BV}, author={Jalowy, Jonas and Stange, Hanna}, year={2026} }'
  chicago: Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point
    Processes.” <i>Stochastic Processes and Their Applications</i> 199 (2026). <a
    href="https://doi.org/10.1016/j.spa.2026.104996">https://doi.org/10.1016/j.spa.2026.104996</a>.
  ieee: 'J. Jalowy and H. Stange, “Box-covariances of hyperuniform point processes,”
    <i>Stochastic Processes and their Applications</i>, vol. 199, Art. no. 104996,
    2026, doi: <a href="https://doi.org/10.1016/j.spa.2026.104996">10.1016/j.spa.2026.104996</a>.'
  mla: Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.”
    <i>Stochastic Processes and Their Applications</i>, vol. 199, 104996, Elsevier
    BV, 2026, doi:<a href="https://doi.org/10.1016/j.spa.2026.104996">10.1016/j.spa.2026.104996</a>.
  short: J. Jalowy, H. Stange, Stochastic Processes and Their Applications 199 (2026).
date_created: 2026-08-04T06:06:09Z
date_updated: 2026-08-04T06:07:59Z
department:
- _id: '94'
doi: 10.1016/j.spa.2026.104996
intvolume: '       199'
language:
- iso: eng
publication: Stochastic Processes and their Applications
publication_identifier:
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier BV
status: public
title: Box-covariances of hyperuniform point processes
type: journal_article
user_id: '113768'
volume: 199
year: '2026'
...
---
_id: '64213'
abstract:
- lang: eng
  text: "A layered graph G^× is the Cartesian product of a graph G = (V, E) with the
    linear graph Z, e.g. Z^× is the 2D square lattice Z^2. For Bernoulli percolation
    with parameter p ∈ [0, 1] on G^× one intuitively would expect that P_p((o, 0)
    ↔ (v, n)) ≥ P_p((o, 0) ↔ (v, n + 1)) for all o, v ∈ V and n ≥ 0. This is reminiscent
    of the better known bunkbed conjecture. Here\r\nwe introduce an approach to the
    above monotonicity conjecture that makes use of a Markov chain building the percolation
    pattern layer by layer. In case of finite G we thus can show that for some N ≥
    0 the above holds\r\nfor all n ≥ N o, v ∈ V and p ∈ [0, 1]. One might hope that
    this Markov chain approach could be useful for other problems concerning Bernoulli
    percolation on layered graphs"
article_number: '104549'
author:
- first_name: Philipp
  full_name: König, Philipp
  last_name: König
- first_name: Thomas
  full_name: Richthammer, Thomas
  id: '62054'
  last_name: Richthammer
citation:
  ama: König P, Richthammer T. Monotonicity properties for Bernoulli percolation on
    layered graphs— A Markov chain approach. <i>Stochastic Processes and their Applications</i>.
    2024;181. doi:<a href="https://doi.org/10.1016/j.spa.2024.104549">10.1016/j.spa.2024.104549</a>
  apa: König, P., &#38; Richthammer, T. (2024). Monotonicity properties for Bernoulli
    percolation on layered graphs— A Markov chain approach. <i>Stochastic Processes
    and Their Applications</i>, <i>181</i>, Article 104549. <a href="https://doi.org/10.1016/j.spa.2024.104549">https://doi.org/10.1016/j.spa.2024.104549</a>
  bibtex: '@article{König_Richthammer_2024, title={Monotonicity properties for Bernoulli
    percolation on layered graphs— A Markov chain approach}, volume={181}, DOI={<a
    href="https://doi.org/10.1016/j.spa.2024.104549">10.1016/j.spa.2024.104549</a>},
    number={104549}, journal={Stochastic Processes and their Applications}, publisher={Elsevier
    BV}, author={König, Philipp and Richthammer, Thomas}, year={2024} }'
  chicago: König, Philipp, and Thomas Richthammer. “Monotonicity Properties for Bernoulli
    Percolation on Layered Graphs— A Markov Chain Approach.” <i>Stochastic Processes
    and Their Applications</i> 181 (2024). <a href="https://doi.org/10.1016/j.spa.2024.104549">https://doi.org/10.1016/j.spa.2024.104549</a>.
  ieee: 'P. König and T. Richthammer, “Monotonicity properties for Bernoulli percolation
    on layered graphs— A Markov chain approach,” <i>Stochastic Processes and their
    Applications</i>, vol. 181, Art. no. 104549, 2024, doi: <a href="https://doi.org/10.1016/j.spa.2024.104549">10.1016/j.spa.2024.104549</a>.'
  mla: König, Philipp, and Thomas Richthammer. “Monotonicity Properties for Bernoulli
    Percolation on Layered Graphs— A Markov Chain Approach.” <i>Stochastic Processes
    and Their Applications</i>, vol. 181, 104549, Elsevier BV, 2024, doi:<a href="https://doi.org/10.1016/j.spa.2024.104549">10.1016/j.spa.2024.104549</a>.
  short: P. König, T. Richthammer, Stochastic Processes and Their Applications 181
    (2024).
date_created: 2026-02-18T12:06:28Z
date_updated: 2026-02-18T12:32:13Z
doi: 10.1016/j.spa.2024.104549
intvolume: '       181'
language:
- iso: eng
publication: Stochastic Processes and their Applications
publication_identifier:
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier BV
status: public
title: Monotonicity properties for Bernoulli percolation on layered graphs— A Markov
  chain approach
type: journal_article
user_id: '62054'
volume: 181
year: '2024'
...
---
_id: '43493'
abstract:
- lang: eng
  text: We consider a measure given as the continuum limit of a one-dimensional Ising
    model with long-range translationally invariant interactions. Mathematically,
    the measure can be described by a self-interacting Poisson driven jump process.
    We prove a correlation inequality, estimating the magnetic susceptibility of this
    model, which holds for small norm of the interaction function. The bound on the
    magnetic susceptibility has applications in quantum field theory and can be used
    to prove existence of ground states for the spin boson model.
article_type: original
author:
- first_name: David
  full_name: Hasler, David
  last_name: Hasler
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Siebert, Oliver
  last_name: Siebert
citation:
  ama: Hasler D, Hinrichs B, Siebert O. Correlation bound for a one-dimensional continuous
    long-range Ising model. <i>Stochastic Processes and their Applications</i>. 2021;146:60-79.
    doi:<a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>
  apa: Hasler, D., Hinrichs, B., &#38; Siebert, O. (2021). Correlation bound for a
    one-dimensional continuous long-range Ising model. <i>Stochastic Processes and
    Their Applications</i>, <i>146</i>, 60–79. <a href="https://doi.org/10.1016/j.spa.2021.12.010">https://doi.org/10.1016/j.spa.2021.12.010</a>
  bibtex: '@article{Hasler_Hinrichs_Siebert_2021, title={Correlation bound for a one-dimensional
    continuous long-range Ising model}, volume={146}, DOI={<a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>},
    journal={Stochastic Processes and their Applications}, publisher={Elsevier BV},
    author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2021},
    pages={60–79} }'
  chicago: 'Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Correlation Bound
    for a One-Dimensional Continuous Long-Range Ising Model.” <i>Stochastic Processes
    and Their Applications</i> 146 (2021): 60–79. <a href="https://doi.org/10.1016/j.spa.2021.12.010">https://doi.org/10.1016/j.spa.2021.12.010</a>.'
  ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Correlation bound for a one-dimensional
    continuous long-range Ising model,” <i>Stochastic Processes and their Applications</i>,
    vol. 146, pp. 60–79, 2021, doi: <a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>.'
  mla: Hasler, David, et al. “Correlation Bound for a One-Dimensional Continuous Long-Range
    Ising Model.” <i>Stochastic Processes and Their Applications</i>, vol. 146, Elsevier
    BV, 2021, pp. 60–79, doi:<a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>.
  short: D. Hasler, B. Hinrichs, O. Siebert, Stochastic Processes and Their Applications
    146 (2021) 60–79.
date_created: 2023-04-14T04:50:01Z
date_updated: 2026-01-16T09:03:28Z
doi: 10.1016/j.spa.2021.12.010
extern: '1'
external_id:
  arxiv:
  - '2104.03013 '
intvolume: '       146'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 60-79
publication: Stochastic Processes and their Applications
publication_identifier:
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier BV
status: public
title: Correlation bound for a one-dimensional continuous long-range Ising model
type: journal_article
user_id: '99427'
volume: 146
year: '2021'
...
---
_id: '40218'
author:
- first_name: R.
  full_name: Lasser, R.
  last_name: Lasser
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Lasser R, Rösler M. Linear mean estimation of weakly stationary stochastic
    processes under the aspects of optimality and asymptotic optimality. <i>Stochastic
    Processes and their Applications</i>. 1991;38(2):279-293. doi:<a href="https://doi.org/10.1016/0304-4149(91)90095-t">10.1016/0304-4149(91)90095-t</a>
  apa: Lasser, R., &#38; Rösler, M. (1991). Linear mean estimation of weakly stationary
    stochastic processes under the aspects of optimality and asymptotic optimality.
    <i>Stochastic Processes and Their Applications</i>, <i>38</i>(2), 279–293. <a
    href="https://doi.org/10.1016/0304-4149(91)90095-t">https://doi.org/10.1016/0304-4149(91)90095-t</a>
  bibtex: '@article{Lasser_Rösler_1991, title={Linear mean estimation of weakly stationary
    stochastic processes under the aspects of optimality and asymptotic optimality},
    volume={38}, DOI={<a href="https://doi.org/10.1016/0304-4149(91)90095-t">10.1016/0304-4149(91)90095-t</a>},
    number={2}, journal={Stochastic Processes and their Applications}, publisher={Elsevier
    BV}, author={Lasser, R. and Rösler, Margit}, year={1991}, pages={279–293} }'
  chicago: 'Lasser, R., and Margit Rösler. “Linear Mean Estimation of Weakly Stationary
    Stochastic Processes under the Aspects of Optimality and Asymptotic Optimality.”
    <i>Stochastic Processes and Their Applications</i> 38, no. 2 (1991): 279–93. <a
    href="https://doi.org/10.1016/0304-4149(91)90095-t">https://doi.org/10.1016/0304-4149(91)90095-t</a>.'
  ieee: 'R. Lasser and M. Rösler, “Linear mean estimation of weakly stationary stochastic
    processes under the aspects of optimality and asymptotic optimality,” <i>Stochastic
    Processes and their Applications</i>, vol. 38, no. 2, pp. 279–293, 1991, doi:
    <a href="https://doi.org/10.1016/0304-4149(91)90095-t">10.1016/0304-4149(91)90095-t</a>.'
  mla: Lasser, R., and Margit Rösler. “Linear Mean Estimation of Weakly Stationary
    Stochastic Processes under the Aspects of Optimality and Asymptotic Optimality.”
    <i>Stochastic Processes and Their Applications</i>, vol. 38, no. 2, Elsevier BV,
    1991, pp. 279–93, doi:<a href="https://doi.org/10.1016/0304-4149(91)90095-t">10.1016/0304-4149(91)90095-t</a>.
  short: R. Lasser, M. Rösler, Stochastic Processes and Their Applications 38 (1991)
    279–293.
date_created: 2023-01-26T09:09:22Z
date_updated: 2023-01-26T17:29:03Z
department:
- _id: '555'
doi: 10.1016/0304-4149(91)90095-t
extern: '1'
intvolume: '        38'
issue: '2'
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
page: 279-293
publication: Stochastic Processes and their Applications
publication_identifier:
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier BV
status: public
title: Linear mean estimation of weakly stationary stochastic processes under the
  aspects of optimality and asymptotic optimality
type: journal_article
user_id: '93826'
volume: 38
year: '1991'
...