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Abstract
In this article, we study the existence of an absorbingstate 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 absorbingstate 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 

Pages (fromto)  11231131 
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 
Bibliographical note
Funding Information:Received by the editors August 13th, 2021; accepted June 13th, 2022. 2010 Mathematics Subject Classification. 82C22, 60K35, 60K37. Key words and phrases. Activated Random Walks, Random Environments, absorbingstate phase transition. The authors would like to thank the anonymous referee for many their suggestions to improve the exposition of this article. A.S. is supported by EPSRC Fellowship EP/N004566/1.
Keywords
 Absorbingstate phase transition
 Activated random walks
 Random environments
ASJC Scopus subject areas
 Statistics and Probability
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 1 Finished

Early Career Fellowship  Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures
Stauffer, A. (PI)
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council