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 2 V a capacity wx ≥ 0, which describes how many inactive particles x can hold, where fwxgx2V is a collection of i.i.d random variables. When G is an amenable graph, we prove that if E[wx] < 1, the model goes through an absorbing-state phase transition and if E[wx] = 1, the model fixates for all λ > 0. Moreover, in the former case, we provide bounds for the critical density that match the ones available in the classical Activated Random Walk.