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

Leandro Chiarini, Alexandre Stauffer

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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.
Original languageEnglish
Pages (from-to)1123-1131
Number of pages8
JournalALEA Latin American Journal of Probability and Mathematical Statistics
Early online date6 Aug 2022
Publication statusE-pub ahead of print - 6 Aug 2022


  • math.PR
  • 82C22, 60K35, 682C2 (Primary), 60K37 (Secondary)


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