UNIVERSALITY OF CUTOFF FOR EXCLUSION WITH RESERVOIRS

• 成果类型: Article
• 署名作者: Salez, Justin
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1600
• 发表日期: 2023
• 页码: 478-494
• 关键词: spectral-gap; mixing time; walk

摘要

We consider the exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the pro-cess, in terms of certain simple spectral statistics of the underlying network. Among other consequences we establish a nonconservative analogue of Al-dous's spectral gap conjecture, and we show that cutoff occurs if and only if the product condition is satisfied. We illustrate this by providing explicit cutoffs on discrete lattices of arbitrary dimensions and boundary conditions which substantially generalize recent one-dimensional results. We also obtain cutoff phenomena in relative entropy, Hilbert norm, separation distance, and supremum norm. Our proof exploits negative dependence in a novel, simple way to reduce the understanding of the whole process to that of single-site marginals. We believe that this approach will find other applications.