Annals of Applied Probability最新文献

Disagreement coupling of Gibbs processes with an application to Poisson approximation 吉布斯过程的不一致耦合及其在泊松近似中的应用

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1916

Moritz Otto

引用次数: 6

Set-valued backward stochastic differential equations 集值倒向随机微分方程

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1896

Çağın Ararat, Jin Ma, Wenqian Wu

引用次数: 5

Construction of Boltzmann and McKean–Vlasov type flows (the sewing lemma approach) Boltzmann和McKean-Vlasov型流的构造(缝纫引理法)

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1894

Aurélien Alfonsi, Vlad Bally

{"title":"Construction of Boltzmann and McKean–Vlasov type flows (the sewing lemma approach)","authors":"Aurélien Alfonsi, Vlad Bally","doi":"10.1214/22-aap1894","DOIUrl":"https://doi.org/10.1214/22-aap1894","url":null,"abstract":"We are concerned with a mixture of Boltzmann and McKean–Vlasov-type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself, and driven by a Poisson point measure with the intensity depending also on the law of the solution. Both the analytical Boltzmann equation and the probabilistic interpretation initiated by Tanaka (Z. Wahrsch. Verw. Gebiete 46 (1978/79) 67–105; J. Fac. Sci., Univ. Tokyo, Sect. IA, Math. 34 (1987) 351–369) have intensively been discussed in the literature for specific models related to the behavior of gas molecules. In this paper, we consider general abstract coefficients that may include mean field effects and then we discuss the link with specific models as well. In contrast with the usual approach in which integral equations are used in order to state the problem, we employ here a new formulation of the problem in terms of flows of self-maps on the space of probability measure endowed with the Wasserstein distance. This point of view already appeared in the framework of rough differential equations. Our results concern existence and uniqueness of the solution, in the formulation of flows, but we also prove that the “flow solution” is a solution of the classical integral weak equation and admits a probabilistic interpretation. Moreover, we obtain stability results and regularity with respect to the time for such solutions. Finally we prove the convergence of empirical measures based on particle systems to the solution of our problem, and we obtain the rate of convergence. We discuss as examples the homogeneous and the inhomogeneous Boltzmann (Enskog) equation with hard potentials.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119568","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}

引用次数: 0

A potential-based construction of the increasing supermartingale coupling 渐增上鞅耦合的基于势的构造

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1907

Erhan Bayraktar, Shuoqing Deng, Dominykas Norgilas

引用次数: 4

Functional central limit theorems for local statistics of spatial birth–death processes in the thermodynamic regime 热力学条件下空间生灭过程局部统计的泛函中心极限定理

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1912

Efe Onaran, Omer Bobrowski, Robert J. Adler

引用次数: 1

Gaussian concentration bounds for stochastic chains of unbounded memory 无界记忆随机链的高斯浓度界

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1893

Jean-Rene Chazottes, Sandro Gallo, Daniel Takahashi

{"title":"Gaussian concentration bounds for stochastic chains of unbounded memory","authors":"Jean-Rene Chazottes, Sandro Gallo, Daniel Takahashi","doi":"10.1214/22-aap1893","DOIUrl":"https://doi.org/10.1214/22-aap1893","url":null,"abstract":"Stochastic chains of unbounded memory (SCUMs) are generalization of Markov chains, also known in the literature as “chains with complete connections” or “g-measures”. We obtain Gaussian concentration bounds (GCB) in this large class of models, for general alphabets, under two different conditions on the kernel: (1) when the sum of its oscillations is less than one, or (2) when the sum of its variations is finite, that is, belongs to ℓ1(N). We also obtain explicit constants as functions of the parameters of the model. Our conditions are sharp in the sense that we exhibit examples of SCUMs that do not have GCB and for which the sum of oscillations is 1+ϵ, or the variation belongs to ℓ1+ϵ(N) for any ϵ>0. These examples are based on the existence of phase transitions. We illustrate our results with four applications. First, we derive a Dvoretzky–Kiefer–Wolfowitz-type inequality which gives a uniform control on the fluctuations of the empirical measure. Second, in the finite-alphabet case, we obtain an upper bound on the d¯-distance between two stationary SCUMs and, as a by-product, we obtain new explicit bounds on the speed of Markovian approximation in d¯. Third, we derive new bounds on the fluctuations of the “plug-in” estimator for entropy. Fourth, we obtain new rate of convergence for the maximum likelihood estimator of conditional probability.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119332","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}

引用次数: 1

Anomalous scaling regime for one-dimensional Mott variable-range hopping 一维Mott变距跳变的异常标度区

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1915

David A. Croydon, Ryoki Fukushima, Stefan Junk

引用次数: 4

Hydrodynamic limit for the Kob–Andersen model kobo - andersen模型的水动力极限

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1898

Assaf Shapira

引用次数: 2

Geometry of random Cayley graphs of Abelian groups 阿贝尔群的随机Cayley图的几何

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1899

Jonathan Hermon, Sam Olesker-Taylor

{"title":"Geometry of random Cayley graphs of Abelian groups","authors":"Jonathan Hermon, Sam Olesker-Taylor","doi":"10.1214/22-aap1899","DOIUrl":"https://doi.org/10.1214/22-aap1899","url":null,"abstract":"Consider the random Cayley graph of a finite Abelian group $G$ with respect to $k$ generators chosen uniformly at random, with $1 ll log k ll log |G|$. Draw a vertex $U sim operatorname{Unif}(G)$. We show that the graph distance $operatorname{dist}(mathsf{id},U)$ from the identity to $U$ concentrates at a particular value $M$, which is the minimal radius of a ball in $mathbb Z^k$ of cardinality at least $|G|$, under mild conditions. In other words, the distance from the identity for all but $o(|G|)$ of the elements of $G$ lies in the interval $[M - o(M), M + o(M)]$. In the regime $k gtrsim log |G|$, we show that the diameter of the graph is also asymptotically $M$. In the spirit of a conjecture of Aldous and Diaconis (1985), this $M$ depends only on $k$ and $|G|$, not on the algebraic structure of $G$. Write $d(G)$ for the minimal size of a generating subset of $G$. We prove that the order of the spectral gap is $|G|^{-2/k}$ when $k - d(G) asymp k$ and $|G|$ lies in a density-$1$ subset of $mathbb N$ or when $k - 2 d(G) asymp k$. This extends, for Abelian groups, a celebrated result of Alon and Roichman (1994). The aforementioned results all hold with high probability over the random Cayley graph.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996634","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}

引用次数: 3

Low-temperature Ising dynamics with random initializations 随机初始化的低温Ising动力学

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1911

Reza Gheissari, Alistair Sinclair

{"title":"Low-temperature Ising dynamics with random initializations","authors":"Reza Gheissari, Alistair Sinclair","doi":"10.1214/22-aap1911","DOIUrl":"https://doi.org/10.1214/22-aap1911","url":null,"abstract":"It is well known that Glauber dynamics on spin systems typically suffer exponential slowdowns at low temperatures. This is due to the emergence of multiple metastable phases in the state space, separated by narrow bottlenecks that are hard for the dynamics to cross. It is a folklore belief that if the dynamics is initialized from an appropriate random mixture of ground states, one for each phase, then convergence to the Gibbs distribution should be much faster. However, such phenomena have largely evaded rigorous analysis, as most tools in the study of Markov chain mixing times are tailored to worst-case initializations. In this paper we develop a general framework towards establishing this conjectured behavior for the Ising model. In the classical setting of the Ising model on an N-vertex torus in Zd, our framework implies that the mixing time for the Glauber dynamics, initialized from a 12-12 mixture of the all-plus and all-minus configurations, is N1+o(1) in dimension d=2, and at most quasi-polynomial in all dimensions d≥3, at all temperatures below the critical one. The key innovation in our analysis is the introduction of the notion of “weak spatial mixing within a phase”, a low-temperature adaptation of the classical concept of weak spatial mixing. We show both that this new notion is strong enough to control the mixing time from the above random initialization (by relating it to the mixing time with plus boundary condition at O(logN) scales), and that it holds at all low temperatures in all dimensions. This framework naturally extends to more general families of graphs. To illustrate this, we use the same approach to establish optimal O(NlogN) mixing for the Ising Glauber dynamics on random regular graphs at sufficiently low temperatures, when initialized from the same random mixture.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136167557","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}

引用次数: 0