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Entanglement percolation and spheres in Zd Zd中的纠缠渗流和球体
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp816
O. Couronne
{"title":"Entanglement percolation and spheres in Zd","authors":"O. Couronne","doi":"10.1214/22-ejp816","DOIUrl":"https://doi.org/10.1214/22-ejp816","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49614268","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
Shaken dynamics on the 3d cubic lattice 三维立方晶格上的振动动力学
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp803
B. Scoppola, A. Troiani, Matteo Veglianti
{"title":"Shaken dynamics on the 3d cubic lattice","authors":"B. Scoppola, A. Troiani, Matteo Veglianti","doi":"10.1214/22-ejp803","DOIUrl":"https://doi.org/10.1214/22-ejp803","url":null,"abstract":"On the space of $pm 1$ spin configurations on the 3$d$-square lattice, we consider the emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities are defined in terms of pair ferromagnetic Ising-type Hamiltonians with nearest neighbor interaction $J$, depending on an additional parameter $q$, measuring the tendency of the system to remain locally in the same state. Odd times and even times have different transition probabilities. We compute the stationary measure of the shaken dynamics and we investigate its relation with the Gibbs measure for the 3$d$ Ising model. It turns out that the two parameters $J$ and $q$ tune the geometry of the underlying lattice. We conjecture the existence of unique line of critical points in $J-q$ plane. By a judicious use of perturbative methods we delimit the region where such curve must lie and we perform numerical simulation to determine it. Our method allows us to find in a unified way the critical values of $J$ for Ising model with first neighbors interaction, defined on a whole class of lattices, intermediate between the two-dimensional hexagonal and the three-dimensional cubic one, such as, for example, the tetrahedral lattice. Finally we estimate the critical exponents of the magnetic susceptibility and show that our model captures a dimensional transition in the geometry of the system at $q = 0$.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46057265","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: 2
Λ-coalescents arising in a population with dormancy ∧-在休眠种群中产生的聚结物
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp739
F. Cordero, Adrián González Casanova, Jason Schweinsberg, M. Wilke-Berenguer
{"title":"Λ-coalescents arising in a population with dormancy","authors":"F. Cordero, Adrián González Casanova, Jason Schweinsberg, M. Wilke-Berenguer","doi":"10.1214/22-ejp739","DOIUrl":"https://doi.org/10.1214/22-ejp739","url":null,"abstract":"Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with N dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake, it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, N individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a Λ -coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all Λ -coalescents that can arise in this framework.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45990884","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: 2
Malliavin calculus for marked binomial processes and applications 标记二项式过程的Malliavin演算及其应用
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp892
Hélène Halconruy
{"title":"Malliavin calculus for marked binomial processes and applications","authors":"Hélène Halconruy","doi":"10.1214/22-ejp892","DOIUrl":"https://doi.org/10.1214/22-ejp892","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41767704","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: 1
Persistence of autoregressive sequences with logarithmic tails 具有对数尾的自回归序列的持续性
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp879
D. Denisov, Gunter Hinrich, Martin Kolb, V. Wachtel
{"title":"Persistence of autoregressive sequences with logarithmic tails","authors":"D. Denisov, Gunter Hinrich, Martin Kolb, V. Wachtel","doi":"10.1214/22-ejp879","DOIUrl":"https://doi.org/10.1214/22-ejp879","url":null,"abstract":"We consider autoregressive sequences Xn = aXn−1 + ξn and Mn = max{aMn−1, ξn} with a constant a ∈ (0, 1) and with positive, independent and identically distributed innovations {ξk}. It is known that if P(ξ1 > x) ∼ d log x with some d ∈ (0,− log a) then the chains {Xn} and {Mn} are null recurrent. We investigate the tail behaviour of recurrence times in this case of logarithmically decaying tails. More precisely, we show that the tails of recurrence times are regularly varying of index −1− d/ log a. We also prove limit theorems for {Xn} and {Mn} conditioned to stay over a fixed level x0. Furthermore, we study tail asymptotics for recurrence times of {Xn} and {Mn} in the case when these chains are positive recurrent and the tail of log ξ1 is subexponential.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44293719","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: 2
Extremes of the stochastic heat equation with additive Lévy noise 具有可加性lsamvy噪声的随机热方程的极值
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp855
Carsten Chong, P. Kevei
{"title":"Extremes of the stochastic heat equation with additive Lévy noise","authors":"Carsten Chong, P. Kevei","doi":"10.1214/22-ejp855","DOIUrl":"https://doi.org/10.1214/22-ejp855","url":null,"abstract":"We analyze the spatial asymptotic properties of the solution to the stochastic heat equation driven by an additive Lévy space-time white noise. For fixed time t > 0 and space x ∈ R we determine the exact tail behavior of the solution both for light-tailed and for heavy-tailed Lévy jump measures. Based on these asymptotics we determine for any fixed time t > 0 the almost-sure growth rate of the solution as |x| → ∞. MSC2020 subject classifications: Primary: 60H15; 60F15; 60G70; secondary: 60G17, 60G51.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46084155","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: 1
Contact processes on general spaces. Models on graphs and on manifolds 一般空间上的接触过程。图和流形上的模型
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp765
S. Pirogov, E. Zhizhina
{"title":"Contact processes on general spaces. Models on graphs and on manifolds","authors":"S. Pirogov, E. Zhizhina","doi":"10.1214/22-ejp765","DOIUrl":"https://doi.org/10.1214/22-ejp765","url":null,"abstract":"The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact processes on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant measures in the critical regime under the condition imposed on the associated Markov jump process. This condition means that any pair of independent trajectories of this jump process run away from each other. The general scheme can be applied to the contact process on the lattice in a heterogeneous and random environments as well as to the contact process on graphs and on manifolds.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43134132","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
The topology of SLEκ is random for κ>4 对于κ bbb4, slek的拓扑结构是随机的
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp871
Stephenie Yearwood
{"title":"The topology of SLEκ is random for κ>4","authors":"Stephenie Yearwood","doi":"10.1214/22-ejp871","DOIUrl":"https://doi.org/10.1214/22-ejp871","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42362433","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
Upper Bounds for Fisher information Fisher信息的上界
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp834
S. Bobkov
{"title":"Upper Bounds for Fisher information","authors":"S. Bobkov","doi":"10.1214/22-ejp834","DOIUrl":"https://doi.org/10.1214/22-ejp834","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47244581","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: 1
Variable speed symmetric random walk driven by the simple symmetric exclusion process 简单对称排斥过程驱动的变速对称随机游动
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/21-ejp735
O. Menezes, Jonathon Peterson, Yong-Xiao Xie
{"title":"Variable speed symmetric random walk driven by the simple symmetric exclusion process","authors":"O. Menezes, Jonathon Peterson, Yong-Xiao Xie","doi":"10.1214/21-ejp735","DOIUrl":"https://doi.org/10.1214/21-ejp735","url":null,"abstract":"We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which the weak quenched limit is constructed as a function of the invariant measure of the environment viewed from the walk. We bypass the need to show the existence of this invariant measure. Instead, we find the limit of the quadratic variation of the walk and give an explicit formula for it.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49627692","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
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