SPECTRAL GAP OF THE SYMMETRIC INCLUSION PROCESS

• 成果类型: Article
• 署名作者: Kim, Seonwoo; Sau, Federico
• 署名单位: Korea Institute for Advanced Study (KIAS); University of Trieste
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2085
• 发表日期: 2024
• 页码: 4899-4920
• 关键词: logarithmic sobolev inequality; conservative spin systems; Duality; walk

摘要

We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulated for the interchange process. Finally, by means of duality techniques, we draw analogous conclusions for an interacting diffusion-like unbounded conservative spin system known as Brownian energy process.