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In this article, we study the existence of an absorbing-state phasetransition 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 $x$ canhold, 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 modelgoes through an absorbing state phase transition and if $\mathbbE[w_x]=\infty$, the model fixates for all $\lambda>0$. Moreover, in the formercase, we provide bounds for the critical density that match the ones availablein the classical Activated Random Walk.

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