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## 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 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.

Original language | English |
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Pages (from-to) | 1123-1131 |

Number of pages | 9 |

Journal | ALEA Latin American Journal of Probability and Mathematical Statistics |

Volume | 19 |

Issue number | 2 |

Early online date | 6 Aug 2022 |

DOIs | |

Publication status | Published - 31 Dec 2022 |

## Keywords

- Absorbing-state phase transition
- Activated random walks
- Random environments

## ASJC Scopus subject areas

- Statistics and Probability

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Dive into the research topics of 'Absorbing-state phase transition and activated random walks with unbounded capacities'. Together they form a unique fingerprint.## Projects

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