THE CRITICAL DENSITY FOR ACTIVATED RANDOM WALKS IS ALWAYS LESS THAN 1

• 成果类型: Article
• 署名作者: Asselah, Amine; Forien, Nicolas; Gaudilliere, Alexandre
• 署名单位: Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Sapienza University Rome; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1674
• 发表日期: 2024
• 页码: 1607-1649
• 关键词: stochastic dynamics; phase; fluctuations

摘要

Activated Random Walks, , on Zd d for any d >= 1, is an interacting particle system, where particles can be in either of two states: active or frozen. Each active particle performs a continuous-time simple random walk during an exponential time of parameter lambda , after which it stays still in the frozen state, until another active particle shares its location, and turns it instantaneously back into activity. This model is known to have a phase transition, and we show that the critical density, controlling the phase transition, is less than one in any dimension and for any value of the sleep rate lambda . We provide upper bounds for the critical density in both the small lambda and large lambda regimes.