Pub Date : 2026-02-01Epub Date: 2025-11-10DOI: 10.1016/j.spa.2025.104826
Franziska Bielert
We prove a rough Itô formula for path-dependent functionals of -Hölder continuous paths for . Our approach combines the sewing lemma and a Taylor approximation in terms of path-dependent derivatives.
{"title":"Rough functional Itô formula","authors":"Franziska Bielert","doi":"10.1016/j.spa.2025.104826","DOIUrl":"10.1016/j.spa.2025.104826","url":null,"abstract":"<div><div>We prove a rough Itô formula for path-dependent functionals of <span><math><mi>α</mi></math></span>-Hölder continuous paths for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Our approach combines the sewing lemma and a Taylor approximation in terms of path-dependent derivatives.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104826"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528792","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: 2025-11-05DOI: 10.1016/j.spa.2025.104815
Christian Hirsch , Takashi Owada
This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable assumptions on the shape of trees. The proof relies on an intermediate result on weak convergence of associated point processes towards a Poisson point process. Additionally, we prove the same type of results for the clique counts. Here, a crucial ingredient includes the expectation asymptotics for clique counts, which itself is a result of independent interest.
{"title":"Limit theorems under heavy-tailed scenario in the age-dependent random connection models","authors":"Christian Hirsch , Takashi Owada","doi":"10.1016/j.spa.2025.104815","DOIUrl":"10.1016/j.spa.2025.104815","url":null,"abstract":"<div><div>This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable assumptions on the shape of trees. The proof relies on an intermediate result on weak convergence of associated point processes towards a Poisson point process. Additionally, we prove the same type of results for the clique counts. Here, a crucial ingredient includes the expectation asymptotics for clique counts, which itself is a result of independent interest.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104815"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528754","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: 2025-10-11DOI: 10.1016/j.spa.2025.104791
Leo Hahn
We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant measure, a useful tool for studying clustering phenomena in out-of-equilibrium statistical mechanics, for different tumbling mechanisms and potentials. An important difference with invariant measures of equilibrium systems are Dirac masses on the boundary of the state space, due to the jamming interactions. Qualitative changes in the invariant measure depending on model parameters are also observed, suggesting, like a growing body of evidence, that run-and-tumble particle systems can be classified into close-to-equilibrium and strongly out-of-equilibrium models. We also study the relaxation properties of the system, which are linked to the timescale at which clustering emerges from an arbitrary initial configuration. When the interaction potential is linear, we show that the total variation distance to the invariant measure decays exponentially and provide sharp bounds on the decay rate. When the interaction potential is harmonic, we give quantitative exponential bounds in a Wasserstein-type distance.
{"title":"Steady state and mixing of two run-and-tumble particles interacting through jamming and attractive forces","authors":"Leo Hahn","doi":"10.1016/j.spa.2025.104791","DOIUrl":"10.1016/j.spa.2025.104791","url":null,"abstract":"<div><div>We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant measure, a useful tool for studying clustering phenomena in out-of-equilibrium statistical mechanics, for different tumbling mechanisms and potentials. An important difference with invariant measures of equilibrium systems are Dirac masses on the boundary of the state space, due to the jamming interactions. Qualitative changes in the invariant measure depending on model parameters are also observed, suggesting, like a growing body of evidence, that run-and-tumble particle systems can be classified into close-to-equilibrium and strongly out-of-equilibrium models. We also study the relaxation properties of the system, which are linked to the timescale at which clustering emerges from an arbitrary initial configuration. When the interaction potential is linear, we show that the total variation distance to the invariant measure decays exponentially and provide sharp bounds on the decay rate. When the interaction potential is harmonic, we give quantitative exponential bounds in a Wasserstein-type distance.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104791"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326465","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: 2025-10-20DOI: 10.1016/j.spa.2025.104796
Antonio Galves , Fernando A. Najman , Marcela Svarc , Claudia D. Vargas
We introduce a new clustering procedure for functional data analysis which can classify independent sets of functional samples by their probabilistic law, i.e. that aims to assign data sets to the same cluster if and only if the data were generated with the same underlying distribution. This method has the virtue of being non-supervised and non-parametric, allowing for exploratory investigation with few assumptions about the data. We also present rigorous finite bounds that give us the effect of the number of samples in each dataset on the classification. We also provide an objective heuristic that consistently selects the best partition in a data-driven manner. We show the performance of the method by clustering simulated datasets generated with different distributions.
{"title":"Clustering functional data sets by law","authors":"Antonio Galves , Fernando A. Najman , Marcela Svarc , Claudia D. Vargas","doi":"10.1016/j.spa.2025.104796","DOIUrl":"10.1016/j.spa.2025.104796","url":null,"abstract":"<div><div>We introduce a new clustering procedure for functional data analysis which can classify independent sets of functional samples by their probabilistic law, i.e. that aims to assign data sets to the same cluster if and only if the data were generated with the same underlying distribution. This method has the virtue of being non-supervised and non-parametric, allowing for exploratory investigation with few assumptions about the data. We also present rigorous finite bounds that give us the effect of the number of samples in each dataset on the classification. We also provide an objective heuristic that consistently selects the best partition in a data-driven manner. We show the performance of the method by clustering simulated datasets generated with different distributions.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104796"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418566","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.2025.104789
Rami Atar
This paper studies a branching-selection model of motionless particles in , with nonlocal branching, introduced by Durrett and Remenik in dimension 1. The assumptions on the fitness function, , and on the inhomogeneous branching distribution, are mild. The evolution equation for the macroscopic density is given by an integro-differential free boundary problem in , in which the free boundary represents the least -value in the population. The main result is the characterization of the limit in probability of the empirical measure process in terms of the unique solution to this free boundary problem.
{"title":"A Durrett–Remenik particle system in Rd","authors":"Rami Atar","doi":"10.1016/j.spa.2025.104789","DOIUrl":"10.1016/j.spa.2025.104789","url":null,"abstract":"<div><div>This paper studies a branching-selection model of motionless particles in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, with nonlocal branching, introduced by Durrett and Remenik in dimension 1. The assumptions on the fitness function, <span><math><mi>F</mi></math></span>, and on the inhomogeneous branching distribution, are mild. The evolution equation for the macroscopic density is given by an integro-differential free boundary problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, in which the free boundary represents the least <span><math><mi>F</mi></math></span>-value in the population. The main result is the characterization of the limit in probability of the empirical measure process in terms of the unique solution to this free boundary problem.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104789"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528752","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: 2025-10-30DOI: 10.1016/j.spa.2025.104814
Ranieri Dugo , Giacomo Giorgio , Paolo Pigato
Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a multivariate version of the fractional Ornstein–Uhlenbeck process. This multivariate Gaussian process is stationary, ergodic and allows for different Hurst exponents on each component. We characterize its correlation matrix and its short and long time asymptotics. Besides the marginal parameters, the cross correlation between one-dimensional marginal components is ruled by two parameters. We consider the problem of their inference, proposing two types of estimator, constructed from discrete observations of the process. We establish their asymptotic theory, in one case in the long time asymptotic setting, in the other case in the infill and long time asymptotic setting. The limit behavior can be asymptotically Gaussian or non-Gaussian, depending on the values of the Hurst exponents of the marginal components. The technical core of the paper relies on the analysis of asymptotic properties of functionals of Gaussian processes, that we establish using Malliavin calculus and Stein’s method. We provide numerical experiments that support our theoretical analysis and also suggest a conjecture on the application of one of these estimators to the multivariate fractional Brownian Motion.
从[F]中引入的多元分数布朗运动的概念出发。Lavancier， A. Philippe和D. Surgailis。向量自相似过程的协方差函数。统计&概率信件，2009]我们定义了分数Ornstein-Uhlenbeck过程的多元版本。这个多元高斯过程是平稳的，遍历的，并且允许在每个分量上有不同的Hurst指数。我们刻画了它的相关矩阵及其短、长时间渐近性。除了边缘参数外，一维边缘分量之间的相互关系还由两个参数决定。我们考虑了他们的推理问题，提出了两种类型的估计量，由过程的离散观测构造。我们建立了它们的渐近理论，一种是在长时间渐近设置下，另一种是在填充和长时间渐近设置下。极限行为可以是渐近高斯或非高斯的，这取决于边缘分量的Hurst指数的值。本文的技术核心是利用Malliavin演算和Stein方法建立高斯过程泛函的渐近性质分析。我们提供了数值实验来支持我们的理论分析，并提出了一个关于这些估计器在多元分数布朗运动中的应用的猜想。
{"title":"The multivariate fractional Ornstein–Uhlenbeck process","authors":"Ranieri Dugo , Giacomo Giorgio , Paolo Pigato","doi":"10.1016/j.spa.2025.104814","DOIUrl":"10.1016/j.spa.2025.104814","url":null,"abstract":"<div><div>Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a multivariate version of the fractional Ornstein–Uhlenbeck process. This multivariate Gaussian process is stationary, ergodic and allows for different Hurst exponents on each component. We characterize its correlation matrix and its short and long time asymptotics. Besides the marginal parameters, the cross correlation between one-dimensional marginal components is ruled by two parameters. We consider the problem of their inference, proposing two types of estimator, constructed from discrete observations of the process. We establish their asymptotic theory, in one case in the long time asymptotic setting, in the other case in the infill and long time asymptotic setting. The limit behavior can be asymptotically Gaussian or non-Gaussian, depending on the values of the Hurst exponents of the marginal components. The technical core of the paper relies on the analysis of asymptotic properties of functionals of Gaussian processes, that we establish using Malliavin calculus and Stein’s method. We provide numerical experiments that support our theoretical analysis and also suggest a conjecture on the application of one of these estimators to the multivariate fractional Brownian Motion.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104814"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528791","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 : 2026-01-01Epub Date: 2025-09-16DOI: 10.1016/j.spa.2025.104777
Zihao Gu , Yiqing Lin , Kun Xu
In this paper, we study a class of reflected backward stochastic differential equations (RBSDE) driven by a marked point process (MPP) with a convex/concave generator. Based on fixed point argument, -method and truncation technique, the well-posedness of this kind of RBSDE with unbounded terminal condition and obstacle is investigated. Besides, we present an application on the pricing of American options via utility maximization, which is solved by constructing an RBSDE with a convex generator.
{"title":"Reflected BSDE driven by a marked point process with a convex/concave generator","authors":"Zihao Gu , Yiqing Lin , Kun Xu","doi":"10.1016/j.spa.2025.104777","DOIUrl":"10.1016/j.spa.2025.104777","url":null,"abstract":"<div><div>In this paper, we study a class of reflected backward stochastic differential equations (RBSDE) driven by a marked point process (MPP) with a convex/concave generator. Based on fixed point argument, <span><math><mi>θ</mi></math></span>-method and truncation technique, the well-posedness of this kind of RBSDE with unbounded terminal condition and obstacle is investigated. Besides, we present an application on the pricing of American options via utility maximization, which is solved by constructing an RBSDE with a convex generator.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104777"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120729","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 : 2026-01-01Epub Date: 2025-09-17DOI: 10.1016/j.spa.2025.104774
Ben Hambly , Philipp Jettkant
We consider a control problem for the nonlinear stochastic Fokker–Planck equation. This equation describes the evolution of the distribution of nonlocally interacting particles affected by a common source of noise. The system is directed by a controller that acts on the drift term with the goal of minimising a cost functional. We establish the well-posedness of the state equation, prove the existence of optimal controls, and formulate a stochastic maximum principle (SMP) that provides necessary and sufficient optimality conditions for the control problem. The adjoint process arising in the SMP is characterised by a nonlocal (semi)linear backward SPDE for which we study existence and uniqueness. We also rigorously connect the control problem for the nonlinear stochastic Fokker–Planck equation to the control of the corresponding McKean–Vlasov SDE that describes the motion of a representative particle. Our work extends existing results for the control of the Fokker–Planck equation to nonlinear and stochastic dynamics. In particular, the sufficient SMP, which we obtain by exploiting the special structure of the Fokker–Planck equation, seems to be novel even in the linear deterministic setting. We illustrate our results with an application to a model of government interventions in financial systems, supplemented by numerical illustrations.
{"title":"Optimal control of the nonlinear stochastic Fokker–Planck equation","authors":"Ben Hambly , Philipp Jettkant","doi":"10.1016/j.spa.2025.104774","DOIUrl":"10.1016/j.spa.2025.104774","url":null,"abstract":"<div><div>We consider a control problem for the nonlinear stochastic Fokker–Planck equation. This equation describes the evolution of the distribution of nonlocally interacting particles affected by a common source of noise. The system is directed by a controller that acts on the drift term with the goal of minimising a cost functional. We establish the well-posedness of the state equation, prove the existence of optimal controls, and formulate a stochastic maximum principle (SMP) that provides necessary and sufficient optimality conditions for the control problem. The adjoint process arising in the SMP is characterised by a nonlocal (semi)linear backward SPDE for which we study existence and uniqueness. We also rigorously connect the control problem for the nonlinear stochastic Fokker–Planck equation to the control of the corresponding McKean–Vlasov SDE that describes the motion of a representative particle. Our work extends existing results for the control of the Fokker–Planck equation to nonlinear and stochastic dynamics. In particular, the sufficient SMP, which we obtain by exploiting the special structure of the Fokker–Planck equation, seems to be novel even in the linear deterministic setting. We illustrate our results with an application to a model of government interventions in financial systems, supplemented by numerical illustrations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104774"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120730","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 : 2026-01-01Epub Date: 2025-07-23DOI: 10.1016/j.spa.2025.104744
Zaoli Chen, Rafał Kulik
We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these estimators. This is achieved by a precise expansion for the difference between the sliding and the disjoint blocks statistics. The rates in the expansion stem from internal clusters and boundary clusters. To obtain these rates we need to extend the existing results on vague convergence of cluster measures. We reveal dichotomous behaviour between small blocks and large blocks scenario.
{"title":"Asymptotic expansions for blocks estimators: PoT framework","authors":"Zaoli Chen, Rafał Kulik","doi":"10.1016/j.spa.2025.104744","DOIUrl":"10.1016/j.spa.2025.104744","url":null,"abstract":"<div><div>We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these estimators. This is achieved by a precise expansion for the difference between the sliding and the disjoint blocks statistics. The rates in the expansion stem from <em>internal clusters</em> and <em>boundary clusters</em>. To obtain these rates we need to extend the existing results on vague convergence of cluster measures. We reveal dichotomous behaviour between <em>small blocks</em> and <em>large blocks</em> scenario.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104744"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269399","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 : 2026-01-01Epub Date: 2025-09-16DOI: 10.1016/j.spa.2025.104776
Eyob Tsegaye
We investigate the mixing time of the capacity symmetric partial exclusion process of Schütz and Sandow with particles on a segment of length , and we show that this process exhibits cutoff at time . We also introduce a related complete multi-species process that we call the shuffle and show that this process exhibits cutoff at time . This extends the celebrated result of Lacoin, which proved cutoff for the symmetric simple exclusion process on a segment of length and the adjacent transposition shuffle.
{"title":"Mixing time and cutoff for the k-SPEP","authors":"Eyob Tsegaye","doi":"10.1016/j.spa.2025.104776","DOIUrl":"10.1016/j.spa.2025.104776","url":null,"abstract":"<div><div>We investigate the mixing time of the capacity <span><math><mi>k</mi></math></span> symmetric partial exclusion process of Schütz and Sandow with <span><math><mi>m</mi></math></span> particles on a segment of length <span><math><mi>N</mi></math></span>, and we show that this process exhibits cutoff at time <span><math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>k</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>log</mo><mi>m</mi></mrow></math></span>. We also introduce a related complete multi-species process that we call the <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>N</mi></mrow></msub></math></span> shuffle and show that this process exhibits cutoff at time <span><math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>k</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>log</mo><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>. This extends the celebrated result of Lacoin, which proved cutoff for the symmetric simple exclusion process on a segment of length <span><math><mi>N</mi></math></span> and the adjacent transposition shuffle.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104776"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108594","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：