Electronic Journal of Probability最新文献_第3页

Wasserstein-p bounds in the central limit theorem under local dependence 局部依赖下中心极限定理中的Wasserstein-p界

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1009

Tianle Liu, Morgane Austern

引用次数: 1

A global large deviation principle for discrete β-ensembles 离散β系综的全局大偏差原理

IF 1.4 3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp977

E. Dimitrov, Hengzhi Zhang

引用次数: 1

Generalized BSDE and reflected BSDE with random time horizon 具有随机时域的广义BSDE和反射BSDE

IF 1.4 3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp927

A. Aksamit, Libo Li, M. Rutkowski

引用次数: 1

Stationary solutions and local equations for interacting diffusions on regular trees 正则树上相互作用扩散的平稳解和局部方程

IF 1.4 3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/22-ejp889

D. Lacker, Jiacheng Zhang

引用次数: 0

Critical window of the symmetric perceptron 对称感知器的临界窗口

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1024

Dylan J. Altschuler

{"title":"Critical window of the symmetric perceptron","authors":"Dylan J. Altschuler","doi":"10.1214/23-ejp1024","DOIUrl":"https://doi.org/10.1214/23-ejp1024","url":null,"abstract":"We study the critical window of the symmetric binary perceptron, or equivalently, random combinatorial discrepancy. Consider the problem of finding a ±1-valued vector σ satisfying ‖Aσ‖∞≤K, where A is an αn×n matrix with iid Gaussian entries. For fixed K, at which constraint densities α is this constraint satisfaction problem (CSP) satisfiable? A sharp threshold was recently established by Perkins and Xu [29], and Abbe, Li, and Sly [2], answering this to first order. Namely, for each K there exists an explicit critical density αc so that for any fixed ϵ>0, with high probability the CSP is satisfiable for αn<(αc−ϵ)n and unsatisfiable for αn>(αc+ϵ)n. This corresponds to a bound of o(n) on the size of the critical window. We sharpen these results significantly, as well as provide exponential tail bounds. Our main result is that, perhaps surprisingly, the critical window is actually at most of order log(n). More precisely, for a large constant C, with high probability the CSP is satisfiable for αn<αcn−Clog(n) and unsatisfiable for αn>αcn+C. These results add the the symmetric perceptron to the short list of CSP models for which a critical window is rigorously known, and to the even shorter list for which this window is known to have nearly constant width.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135211811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Law of the SLE tip SLE提示法

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1015

Oleg Butkovsky, Vlad Margarint, Yizheng Yuan

引用次数: 1

Irreversible Markov dynamics and hydrodynamics for KPZ states in the stochastic six vertex model 随机六顶点模型中KPZ状态的不可逆马尔可夫动力学和流体力学

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1005

Matthew Nicoletti, Leonid Petrov

{"title":"Irreversible Markov dynamics and hydrodynamics for KPZ states in the stochastic six vertex model","authors":"Matthew Nicoletti, Leonid Petrov","doi":"10.1214/23-ejp1005","DOIUrl":"https://doi.org/10.1214/23-ejp1005","url":null,"abstract":"We introduce a family of Markov growth processes on discrete height functions defined on the 2-dimensional square lattice. Each height function corresponds to a configuration of the six vertex model on the infinite square lattice. We focus on the stochastic six vertex model corresponding to a particular two-parameter family of weights within the ferroelectric (Δ>1) regime. It is believed (and partially proven, see Aggarwal [3]) that the stochastic six vertex model displays nontrivial pure (i.e., translation invariant and ergodic) Gibbs states of two types, KPZ and liquid. These phases have very different long-range correlation structures. The Markov processes we construct preserve the KPZ pure states in the full plane. We also show that the same processes put on the torus preserve arbitrary Gibbs measures for generic six vertex weights (not necessarily in the ferroelectric regime). Our dynamics arise naturally from the Yang–Baxter equation for the six vertex model. Using the bijectivisation of the Yang–Baxter equation introduced in Bufetov–Petrov [17], we first construct discrete time dynamics on six vertex configurations with a particular boundary condition, namely with the step initial condition in the quarter plane. Then we take a Poisson-type limit to obtain simpler continuous time dynamics. These dynamics are irreversible; in particular, the height function has a nonzero average drift. In each KPZ pure state, we explicitly compute the average drift (also known as the current) as a function of the slope. We use this to heuristically analyze the hydrodynamics of a non-stationary version of our process acting on quarter plane stochastic six vertex configurations.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"2020 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135660604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Time-reversal of multiple-force-point chordal SLEκ(ρ_) 多力点弦态slek (ρ_)的时间反演

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1040

Pu Yu

引用次数: 1

Exponential ergodicity and propagation of chaos for path-distribution dependent stochastic Hamiltonian system 路径-分布相关随机哈密顿系统的指数遍历性与混沌的传播

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1027

Xing Huang, Wujun Lv

引用次数: 2

Scaling limit for line ensembles of random walks with geometric area tilts 具有几何面积倾斜的随机漫步线集合的尺度限制

3区数学

Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1026

Christian Serio

{"title":"Scaling limit for line ensembles of random walks with geometric area tilts","authors":"Christian Serio","doi":"10.1214/23-ejp1026","DOIUrl":"https://doi.org/10.1214/23-ejp1026","url":null,"abstract":"We consider line ensembles of non-intersecting random walks constrained by a hard wall, each tilted by the area underneath it with geometrically growing pre-factors bi where b>1. This is a model for the level lines of the (2+1)D SOS model above a hard wall, which itself mimics the low-temperature 3D Ising interface. A similar model with b=1 and a fixed number of curves was studied by Ioffe, Velenik, and Wachtel (2018), who derived a scaling limit as the time interval [−N,N] tends to infinity. Line ensembles of Brownian bridges with geometric area tilts (b>1) were studied by Caputo, Ioffe, and Wachtel (2019), and later by Dembo, Lubetzky, and Zeitouni (2022+). Their results show that as the time interval and the number of curves n tend to infinity, the top k paths converge to a limiting measure μ. In this paper we address the open problem of proving existence of a scaling limit for random walk ensembles with geometric area tilts. We prove that with mild assumptions on the jump distribution, under suitable scaling the top k paths converge to the same measure μ as N→∞ followed by n→∞. We do so both in the case of bridges fixed at ±N and of walks fixed only at −N.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135261330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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