具有无限容量的吸收态相变和激活随机游动

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
L. Chiarini, Alexandre O. Stauffer
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引用次数: 0

摘要

在本文中,我们研究了推广激活随机游动(ARW)的阿贝尔过程的吸收态相变的存在性。给定顶点传递性$G=(V,E)$,我们将容量$w_x\ge0$关联到V$中的每个站点$x\,该容量描述了$x$可以容纳多少非活动粒子,其中$\{w_x\}_{x\inV}$是i.i.d随机变量的集合。当$G$是一个可调和图时,我们证明了如果$\mathbb E[w_x]0$。此外,在前一种情况下,我们提供了与经典激活随机漫步中可用的临界密度相匹配的临界密度的边界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Absorbing-state phase transition and activated random walks with unbounded capacities
In this article, we study the existence of an absorbing-state phase transition of an Abelian process that generalises the Activated Random Walk (ARW). Given a vertex transitive $G=(V,E)$, we associate to each site $x \in V$ a capacity $w_x \ge 0$, which describes how many inactive particles $x$ can hold, where $\{w_x\}_{x \in V}$ is a collection of i.i.d random variables. When $G$ is an amenable graph, we prove that if $\mathbb E[w_x]<\infty$, the model goes through an absorbing state phase transition and if $\mathbb E[w_x]=\infty$, the model fixates for all $\lambda>0$. Moreover, in the former case, we provide bounds for the critical density that match the ones available in the classical Activated Random Walk.
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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