ENTROPY DISSIPATION ESTIMATES FOR INHOMOGENEOUS ZERO-RANGE PROCESSES

• 成果类型: Article
• 署名作者: Hermon, Jonathan; Salez, Justin
• 署名单位: University of British Columbia; Universite PSL; Universite Paris-Dauphine; Universite PSL
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1646
• 发表日期: 2021
• 页码: 2275-2283
• 关键词: logarithmic sobolev inequality; spectral-gap; relaxation; constant; DYNAMICS; bounds; decay

摘要

Introduced by Lu and Yau (Comm. Math. Phys. 156 (1993) 399-433), the martingale decomposition method is a powerful recursive strategy that has produced sharp log-Sobolev inequalities for homogeneous particle systems. However, the intractability of certain covariance terms has so far precluded applications to heterogeneous models. Here we demonstrate that the existence of an appropriate coupling can be exploited to bypass this limitation effortlessly. Our main result is a dimension-free modified log-Sobolev inequality for zero-range processes on the complete graph, under the only requirement that all rate increments lie in a compact subset of (0,infinity). This settles an open problem raised by Caputo and Posta (Probab. Theory Related Fields 139 (2007) 65-87) and reiterated by Caputo, Dai Pra and Posta (Ann. Inst. Henri Poincare Probab. Stat. 45 (2009) 734-753). We believe that our approach is simple enough to be applicable to many systems.