SEPARATION CUTOFF FOR ACTIVATED RANDOM WALKS

• 成果类型: Article
• 署名作者: Bristiel, Alexandre; Salez, Justin
• 署名单位: Universite PSL; Universite Paris-Dauphine; Universite PSL
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2089
• 发表日期: 2024
• 页码: 5211-5227
• 关键词: phase; UNIVERSALITY; density; times

摘要

We consider activated random walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the nonreversibility of the dynamics and the lack of knowledge on the stationary distribution, we explicitly determine the relaxation time of the process, and prove that separation cutoff is equivalent to the product condition. We also provide sharp estimates on the center and width of the cutoff window. Finally, we illustrate those results by establishing explicit separation cutoffs on various networks, including: (i) large finite subgraphs of any fixed infinite nonamenable graph, with absorption at the boundary and (ii) large finite vertex-transitive graphs with absorption at a single vertex. The latter result settles a conjecture of Levine and Liang. Our proofs rely on the refined analysis of a strong stationary time recently discovered by Levine and Liang and involving the IDLA process.