Absorbing-state phase transition and activated random walks with unbounded capacities

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-08-06 DOI:10.30757/alea.v19-46
L. Chiarini, Alexandre O. Stauffer
{"title":"Absorbing-state phase transition and activated random walks with unbounded capacities","authors":"L. Chiarini, Alexandre O. Stauffer","doi":"10.30757/alea.v19-46","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v19-46","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

Abstract

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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
具有无限容量的吸收态相变和激活随机游动
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。
求助全文
约1分钟内获得全文 去求助
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.
期刊最新文献
Quantitative Multidimensional Central Limit Theorems for Means of the Dirichlet-Ferguson Measure Characterizations of multivariate distributions with limited memory revisited: An analytical approach Sojourn times of Gaussian and related random fields On the existence of maximum likelihood estimates for the parameters of the Conway-Maxwell-Poisson distribution Asymptotic formula for the conjunction probability of smooth stationary Gaussian fields
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1