Annals of Probability最新文献_第9页

An $L^{p}$ theory of sparse graph convergence II: LD convergence, quotients and right convergence 稀疏图收敛的一个L^{p}$理论II: LD收敛、商和右收敛

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-08-04 DOI: 10.1214/17-AOP1187

C. Borgs, J. Chayes, Henry Cohn, Yufei Zhao

引用次数: 84

Mean field games with common noise 平均场游戏与共同的噪音

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-07-23 DOI: 10.1214/15-AOP1060

R. Carmona, F. Delarue, D. Lacker

引用次数: 208

Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients 具有局部Sobolev和超线性增长系数的SDEs的Sobolev可微流

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-07-22 DOI: 10.1214/15-AOP1057

Longjie Xie, Xicheng Zhang

引用次数: 44

Universality of cutoff for the ising model ising模型的截止的通用性

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-07-07 DOI: 10.1214/16-AOP1146

E. Lubetzky, A. Sly

{"title":"Universality of cutoff for the ising model","authors":"E. Lubetzky, A. Sly","doi":"10.1214/16-AOP1146","DOIUrl":"https://doi.org/10.1214/16-AOP1146","url":null,"abstract":"On any locally-finite geometry, the stochastic Ising model is known to be contractive when the inverse-temperature ββ is small enough, via classical results of Dobrushin and of Holley in the 1970s. By a general principle proposed by Peres, the dynamics is then expected to exhibit cutoff. However, so far cutoff for the Ising model has been confirmed mainly for lattices, heavily relying on amenability and log Sobolev inequalities. Without these, cutoff was unknown at any fixed β>0β>0, no matter how small, even in basic examples such as the Ising model on a binary tree or a random regular graph.We use the new framework of information percolation to show that, in any geometry, there is cutoff for the Ising model at high enough temperatures. Precisely, on any sequence of graphs with maximum degree dd, the Ising model has cutoff provided that β<κ/dβ<κ/d for some absolute constant κκ (a result which, up to the value of κκ, is best possible). Moreover, the cutoff location is established as the time at which the sum of squared magnetizations drops to 1, and the cutoff window is O(1)O(1), just as when β=0β=0.Finally, the mixing time from almost every initial state is not more than a factor of 1+eβ1+eβ faster then the worst one (with eβ→0eβ→0 as β→0β→0), whereas the uniform starting state is at least 2−eβ2−eβ times faster.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2014-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1146","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66047787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 25

Bulk universality for deformed Wigner matrices 变形Wigner矩阵的体通用性

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-05-26 DOI: 10.1214/15-AOP1023

J. Lee, Kevin Schnelli, Ben Stetler, H. Yau

引用次数: 74

A Gaussian upper bound for martingale small-ball probabilities 鞅小球概率的高斯上界

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-05-23 DOI: 10.1214/15-AOP1073

James R. Lee, Y. Peres, Charles K. Smart

引用次数: 12

Intermittency for branching random walk in Pareto environment Pareto环境下分支随机漫步的间歇性问题

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-05-21 DOI: 10.1214/15-AOP1021

Marcel Ortgiese, Matthew I. Roberts

引用次数: 12

Extremes of a class of nonhomogeneous Gaussian random fields 一类非齐次高斯随机场的极值

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-05-12 DOI: 10.1214/14-AOP994

Krzysztof Dcebicki, E. Hashorva, L. Ji

引用次数: 36

A noncommutative martingale convexity inequality 一个非交换鞅凸性不等式

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-05-02 DOI: 10.1214/14-AOP990

'Eric Ricard, Quanhua Xu

引用次数: 41

Relaxation to equilibrium of generalized East processes on $mathbb{Z}^{d}$: Renormalization group analysis and energy-entropy competition $mathbb{Z}^{d}$上广义East过程的松弛平衡:重整化群分析和能量熵竞争

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-04-29 DOI: 10.1214/15-AOP1011

P. Chleboun, A. Faggionato, F. Martinelli

{"title":"Relaxation to equilibrium of generalized East processes on $mathbb{Z}^{d}$: Renormalization group analysis and energy-entropy competition","authors":"P. Chleboun, A. Faggionato, F. Martinelli","doi":"10.1214/15-AOP1011","DOIUrl":"https://doi.org/10.1214/15-AOP1011","url":null,"abstract":"We consider a class of kinetically constrained interacting particle systems on Zd which play a key role in several heuristic qualitative and quantitative approaches to describe the complex behavior of glassy dynamics. With rate one and independently among the vertices of Zd, to each occupation variable ηx∈{0,1} a new value is proposed by tossing a (1−q)-coin. If a certain local constraint is satisfied by the current configuration the proposed move is accepted, otherwise it is rejected. For d=1, the constraint requires that there is a vacancy at the vertex to the left of the updating vertex. In this case, the process is the well-known East process. On Z2, the West or the South neighbor of the updating vertex must contain a vacancy, similarly, in higher dimensions. Despite of their apparent simplicity, in the limit q↘0 of low vacancy density, corresponding to a low temperature physical setting, these processes feature a rather complicated dynamic behavior with hierarchical relaxation time scales, heterogeneity and universality. Using renormalization group ideas, we first show that the relaxation time on Zd scales as the 1/d-root of the relaxation time of the East process, confirming indications coming from massive numerical simulations. Next, we compute the relaxation time in finite boxes by carefully analyzing the subtle energy-entropy competition, using a multiscale analysis, capacity methods and an algorithmic construction. Our results establish dynamic heterogeneity and a dramatic dependence on the boundary conditions. Finally, we prove a rather strong anisotropy property of these processes: the creation of a new vacancy at a vertex x out of an isolated one at the origin (a seed) may occur on (logarithmically) different time scales which heavily depend not only on the l1-norm of x but also on its direction.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2014-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66031627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 22