We establish a limit theorem for a new model of 3-dimensional random walk in an inhomogeneous lattice with random orientations. This model can be seen as a 3-dimensional version of the Matheron and de Marsily model [1]. This new model leads us naturally to the study of iterated random walk in random scenery, which is a new process that can be described as a random walk in random scenery evolving in a second random scenery. We use the french acronym PAPAPA for this process unprecedented in literature, and answer a question about its stochastic behaviour asked about twenty years ago by Stéphane Le Borgne.
{"title":"Iterated random walks in random scenery (PAPAPA)","authors":"Nadine Guillotin-Plantard , Françoise Pène , Frédérique Watbled","doi":"10.1016/j.spa.2025.104843","DOIUrl":"10.1016/j.spa.2025.104843","url":null,"abstract":"<div><div>We establish a limit theorem for a new model of 3-dimensional random walk in an inhomogeneous lattice with random orientations. This model can be seen as a 3-dimensional version of the Matheron and de Marsily model [1]. This new model leads us naturally to the study of iterated random walk in random scenery, which is a new process that can be described as a random walk in random scenery evolving in a second random scenery. We use the french acronym PAPAPA for this process unprecedented in literature, and answer a question about its stochastic behaviour asked about twenty years ago by Stéphane Le Borgne.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104843"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-29DOI: 10.1016/j.spa.2025.104835
Bruno Costacèque, Laurent Decreusefond
The functional characterization of a measure, an essential but delicate aspect of Stein’s method, is shown to be accessible for stable probability distributions on convex cones. This notion encompasses the usual stable distributions e.g. Gaussian, Pareto, etc. but also the max-stable distributions: Weibull, Gumbel and Fréchet. We use the definition of max-stability to define a Markov process whose invariant measure is the stable measure of interest. In this paper, we focus on the Gumbel distribution and show how this construction can be applied to estimate the rate of convergence in the classical coupon collector’s problem.
{"title":"Convergence rate for the coupon collector’s problem with Stein’s method","authors":"Bruno Costacèque, Laurent Decreusefond","doi":"10.1016/j.spa.2025.104835","DOIUrl":"10.1016/j.spa.2025.104835","url":null,"abstract":"<div><div>The functional characterization of a measure, an essential but delicate aspect of Stein’s method, is shown to be accessible for stable probability distributions on convex cones. This notion encompasses the usual stable distributions <em>e.g.</em> Gaussian, Pareto, <em>etc.</em> but also the max-stable distributions: Weibull, Gumbel and Fréchet. We use the definition of max-stability to define a Markov process whose invariant measure is the stable measure of interest. In this paper, we focus on the Gumbel distribution and show how this construction can be applied to estimate the rate of convergence in the classical coupon collector’s problem.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104835"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-15DOI: 10.1016/j.spa.2025.104851
Arnaud Guillin , Boris Nectoux , Liming Wu
In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. Cépa and D. Lépingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].
{"title":"Quasi-stationarity of the Dyson Brownian motion with collisions","authors":"Arnaud Guillin , Boris Nectoux , Liming Wu","doi":"10.1016/j.spa.2025.104851","DOIUrl":"10.1016/j.spa.2025.104851","url":null,"abstract":"<div><div>In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. Cépa and D. Lépingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104851"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-11DOI: 10.1016/j.spa.2025.104849
Armand Bernou , Mitia Duerinckx , Matthieu Ménard
We consider a system of N Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable N-particle distribution. In this model framework, we establish a fine version of the so-called creation-of-chaos phenomenon: in weak norms, the mean-field approximation for a typical particle is shown to hold with an accuracy up to an error due solely to initial pair correlations, which is damped exponentially over time. Corresponding higher-order results are also derived in the form of higher-order correlation estimates. The approach is new and easily adaptable: we start from suboptimal correlation estimates obtained from an elementary use of Itô’s calculus on moments of the empirical measure, together with ergodic properties of the mean-field dynamics, and these bounds are then made optimal after combination with PDE estimates on the BBGKY hierarchy.
{"title":"Creation of chaos for interacting Brownian particles","authors":"Armand Bernou , Mitia Duerinckx , Matthieu Ménard","doi":"10.1016/j.spa.2025.104849","DOIUrl":"10.1016/j.spa.2025.104849","url":null,"abstract":"<div><div>We consider a system of <em>N</em> Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable <em>N</em>-particle distribution. In this model framework, we establish a fine version of the so-called creation-of-chaos phenomenon: in weak norms, the mean-field approximation for a typical particle is shown to hold with an accuracy <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> up to an error due solely to initial pair correlations, which is damped exponentially over time. Corresponding higher-order results are also derived in the form of higher-order correlation estimates. The approach is new and easily adaptable: we start from suboptimal correlation estimates obtained from an elementary use of Itô’s calculus on moments of the empirical measure, together with ergodic properties of the mean-field dynamics, and these bounds are then made optimal after combination with PDE estimates on the BBGKY hierarchy.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104849"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-24DOI: 10.1016/j.spa.2025.104813
Elena Bandini , Christian Keller
We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton–Jacobi–Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations.
{"title":"Non-local Hamilton–Jacobi–Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes","authors":"Elena Bandini , Christian Keller","doi":"10.1016/j.spa.2025.104813","DOIUrl":"10.1016/j.spa.2025.104813","url":null,"abstract":"<div><div>We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton–Jacobi–Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104813"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-15DOI: 10.1016/j.spa.2025.104834
Haojie Hou , Yan-Xia Ren , Renming Song
<div><div>Consider a one dimensional critical branching Lévy process <span><math><mrow><mo>(</mo><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow></math></span>. Assume that the offspring distribution either has finite second moment or belongs to the domain of attraction of some <span><math><mi>α</mi></math></span>-stable distribution with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, and that the underlying Lévy process <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> is non-lattice and has finite <span><math><mrow><mn>2</mn><mo>+</mo><msup><mrow><mi>δ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> moment for some <span><math><mrow><msup><mrow><mi>δ</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>></mo><mn>0</mn></mrow></math></span>. We first prove that <span><span><span><math><mrow><msup><mrow><mi>t</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup><mfenced><mrow><mn>1</mn><mo>−</mo><msub><mrow><mi>E</mi></mrow><mrow><msqrt><mrow><mi>t</mi></mrow></msqrt><mi>y</mi></mrow></msub><mfenced><mrow><mo>exp</mo><mfenced><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mrow></mfrac><mo>∫</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup></mrow></mfrac><mo>∫</mo><mi>g</mi><mfenced><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><msqrt><mrow><mi>t</mi></mrow></msqrt></mrow></mfrac></mrow></mfenced><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow></mrow></mfenced></mrow></mfenced></mrow></mfenced></mrow></math></span></span></span>converges as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span> for any non-negative bounded Lipschitz function <span><math><mi>g</mi></math></span> and any non-negative directly Riemann integrable function <span><math><mi>h</mi></math></span> of compact support. Then for any <span><math><mrow><mi>y</mi><mo>∈</mo><mi>R</mi></mrow></math></span> and bounded Borel set <span><math><mi>A</mi></math></span> of positive Lebesgue measure with its boundary having zero Lebesgue measure,
{"title":"Local properties for 1-dimensional critical branching Lévy process","authors":"Haojie Hou , Yan-Xia Ren , Renming Song","doi":"10.1016/j.spa.2025.104834","DOIUrl":"10.1016/j.spa.2025.104834","url":null,"abstract":"<div><div>Consider a one dimensional critical branching Lévy process <span><math><mrow><mo>(</mo><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow></math></span>. Assume that the offspring distribution either has finite second moment or belongs to the domain of attraction of some <span><math><mi>α</mi></math></span>-stable distribution with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, and that the underlying Lévy process <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> is non-lattice and has finite <span><math><mrow><mn>2</mn><mo>+</mo><msup><mrow><mi>δ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> moment for some <span><math><mrow><msup><mrow><mi>δ</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>></mo><mn>0</mn></mrow></math></span>. We first prove that <span><span><span><math><mrow><msup><mrow><mi>t</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup><mfenced><mrow><mn>1</mn><mo>−</mo><msub><mrow><mi>E</mi></mrow><mrow><msqrt><mrow><mi>t</mi></mrow></msqrt><mi>y</mi></mrow></msub><mfenced><mrow><mo>exp</mo><mfenced><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mrow></mfrac><mo>∫</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup></mrow></mfrac><mo>∫</mo><mi>g</mi><mfenced><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><msqrt><mrow><mi>t</mi></mrow></msqrt></mrow></mfrac></mrow></mfenced><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow></mrow></mfenced></mrow></mfenced></mrow></mfenced></mrow></math></span></span></span>converges as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span> for any non-negative bounded Lipschitz function <span><math><mi>g</mi></math></span> and any non-negative directly Riemann integrable function <span><math><mi>h</mi></math></span> of compact support. Then for any <span><math><mrow><mi>y</mi><mo>∈</mo><mi>R</mi></mrow></math></span> and bounded Borel set <span><math><mi>A</mi></math></span> of positive Lebesgue measure with its boundary having zero Lebesgue measure, ","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104834"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145578989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-21DOI: 10.1016/j.spa.2025.104807
Shukai Chen , Rongjuan Fang , Lina Ji , Jian Wang
We establish the exponential ergodicity in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and other mild assumptions. The proof is based on a Markov coupling process along with some delicate estimates for the associated coupling generator. In particular, the main result indicates whether and how the competition mechanism, the random environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the processes.
{"title":"Exponential ergodicity of CBIRE-processes with competition and catastrophes","authors":"Shukai Chen , Rongjuan Fang , Lina Ji , Jian Wang","doi":"10.1016/j.spa.2025.104807","DOIUrl":"10.1016/j.spa.2025.104807","url":null,"abstract":"<div><div>We establish the exponential ergodicity in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and other mild assumptions. The proof is based on a Markov coupling process along with some delicate estimates for the associated coupling generator. In particular, the main result indicates whether and how the competition mechanism, the random environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104807"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-24DOI: 10.1016/j.spa.2025.104792
Ahmed El Alaoui
We show that in the Ising pure -spin model of spin glasses, shattering takes place at all inverse temperatures when is sufficiently large as a function of . Of special interest is the lower boundary of this interval which matches the large asymptotics of the inverse temperature marking the hypothetical dynamical transition predicted in statistical physics. We show this as a consequence of a ‘soft’ version of the overlap gap property which asserts the existence of a distance gap of points of typical energy from a typical sample from the Gibbs measure. We further show that this latter property implies that stable algorithms seeking to return a point of at least typical energy are confined to an exponentially rare subset of that super-level set, provided that their success probability is not vanishingly small.
{"title":"Near-optimal shattering in the Ising pure p-spin and rarity of solutions returned by stable algorithms","authors":"Ahmed El Alaoui","doi":"10.1016/j.spa.2025.104792","DOIUrl":"10.1016/j.spa.2025.104792","url":null,"abstract":"<div><div>We show that in the Ising pure <span><math><mi>p</mi></math></span>-spin model of spin glasses, shattering takes place at all inverse temperatures <span><math><mrow><mi>β</mi><mo>∈</mo><mrow><mo>(</mo><msqrt><mrow><mrow><mo>(</mo><mn>2</mn><mo>log</mo><mi>p</mi><mo>)</mo></mrow><mo>/</mo><mi>p</mi></mrow></msqrt><mo>,</mo><msqrt><mrow><mn>2</mn><mo>log</mo><mn>2</mn></mrow></msqrt><mo>)</mo></mrow></mrow></math></span> when <span><math><mi>p</mi></math></span> is sufficiently large as a function of <span><math><mi>β</mi></math></span>. Of special interest is the lower boundary of this interval which matches the large <span><math><mi>p</mi></math></span> asymptotics of the inverse temperature marking the hypothetical dynamical transition predicted in statistical physics. We show this as a consequence of a ‘soft’ version of the overlap gap property which asserts the existence of a distance gap of points of typical energy from a typical sample from the Gibbs measure. We further show that this latter property implies that stable algorithms seeking to return a point of at least typical energy are confined to an exponentially rare subset of that super-level set, provided that their success probability is not vanishingly small.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104792"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-14DOI: 10.1016/j.spa.2025.104793
Oleksii Galganov , Andrii Ilienko
The Chinese restaurant process is a basic sequential construction of consistent random partitions. We consider random point measures describing the composition of small blocks in such partitions and show that their scaling limit is given by the projective limit of certain inhomogeneous Poisson measures on cones of increasing dimension. This result makes it possible to derive classical and functional limit theorems in the Skorokhod topology for various characteristics of the Chinese restaurant process.
{"title":"Scaling limit for small blocks in the Chinese restaurant process","authors":"Oleksii Galganov , Andrii Ilienko","doi":"10.1016/j.spa.2025.104793","DOIUrl":"10.1016/j.spa.2025.104793","url":null,"abstract":"<div><div>The Chinese restaurant process is a basic sequential construction of consistent random partitions. We consider random point measures describing the composition of small blocks in such partitions and show that their scaling limit is given by the projective limit of certain inhomogeneous Poisson measures on cones of increasing dimension. This result makes it possible to derive classical and functional limit theorems in the Skorokhod topology for various characteristics of the Chinese restaurant process.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104793"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-16DOI: 10.1016/j.spa.2025.104795
Jules Berry , Fausto Colantoni
In this paper, we investigate continuous diffusions on star graphs with sticky behaviour at the vertex. These are Markov processes with continuous paths having a positive occupation time at the vertex. We characterize the sticky diffusions as time changed nonsticky diffusions by adapting the classical technique of Itô and McKean. We prove a form of Itô formula, also known as Freidlin–Sheu formula, for this type of process. As an intermediate step, we also obtain a stochastic differential equation satisfied by the radial component of the process. These results generalize those already known for sticky diffusions on a half-line and skew sticky diffusions on the real line.
{"title":"Sticky diffusions on star graphs: Characterization and Itô formula","authors":"Jules Berry , Fausto Colantoni","doi":"10.1016/j.spa.2025.104795","DOIUrl":"10.1016/j.spa.2025.104795","url":null,"abstract":"<div><div>In this paper, we investigate continuous diffusions on star graphs with sticky behaviour at the vertex. These are Markov processes with continuous paths having a positive occupation time at the vertex. We characterize the sticky diffusions as time changed nonsticky diffusions by adapting the classical technique of Itô and McKean. We prove a form of Itô formula, also known as Freidlin–Sheu formula, for this type of process. As an intermediate step, we also obtain a stochastic differential equation satisfied by the radial component of the process. These results generalize those already known for sticky diffusions on a half-line and skew sticky diffusions on the real line.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104795"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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