A VERSION OF ALDOUS' SPECTRAL-GAP CONJECTURE FOR THE ZERO RANGE PROCESS

• 成果类型: Article
• 署名作者: Hermon, Jonathan; Salez, Justin
• 署名单位: University of Cambridge; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1449
• 发表日期: 2019
• 页码: 2217-2229
• 关键词: mixing times

摘要

We show that the spectral gap of a general zero range process can be controlled in terms of the spectral gap for a single particle. This is in the spirit of Aldous' famous spectral-gap conjecture for the interchange process, now resolved by Caputo et al. Our main inequality decouples the role of the geometry (defined by the jump matrix) from that of the kinetics (specified by the exit rates). Among other consequences, the various spectral gap estimates that were so far only available on the complete graph or the d-dimensional torus now extend effortlessly to arbitrary geometries. As an illustration, we determine the exact order of magnitude of the spectral gap of the rate-one zero-range process on any regular graph and, more generally, for any doubly stochastic jump matrix.