It has been conjectured that the critical density of the Activated Random Walk model is strictly less than one for any value of the sleeping rate. We prove this conjecture on ℤd when d ≥ 3 and, more generally, on graphs where the random walk is transient. Moreover, we establish the occurrence of a phase transition on non-amenable graphs, extending previous results which require that the graph is amenable or a regular tree.
Active phase for activated random walks on ℤd, d ≥ 3, with density less than one and arbitrary sleeping rate / Taggi, L.. - In: ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. - ISSN 0246-0203. - 55:3(2019), pp. 1751-1764. [10.1214/18-AIHP933]
Active phase for activated random walks on ℤd, d ≥ 3, with density less than one and arbitrary sleeping rate
Taggi L.
2019
Abstract
It has been conjectured that the critical density of the Activated Random Walk model is strictly less than one for any value of the sleeping rate. We prove this conjecture on ℤd when d ≥ 3 and, more generally, on graphs where the random walk is transient. Moreover, we establish the occurrence of a phase transition on non-amenable graphs, extending previous results which require that the graph is amenable or a regular tree.| File | Dimensione | Formato | |
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