@techreport{b962772e1915405c8e488b0615d8aaac,

title = "Absorbing-state phase transition and activated random walks with unbounded capacities",

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 $\mathbb E[w_x]0$. Moreover, in the former case, we provide bounds for the critical density that match the ones available in the classical Activated Random Walk. ",

keywords = "math.PR, 82C22, 60K35, 682C2 (Primary), 60K37 (Secondary)",

author = "Leandro Chiarini and Alexandre Stauffer",

note = "11 pages, 1 figure",

year = "2021",

month = aug,

day = "6",

language = "English",

series = "ArXiv e-prints",

publisher = "arXiv",

type = "WorkingPaper",

institution = "arXiv",

}