Entropy dissipation estimates for inhomogeneous zero-range processes
Hermon, Jonathan; Salez, Justin (2021), Entropy dissipation estimates for inhomogeneous zero-range processes, Annals of Applied Probability, 31, 5, p. 2275-2283. 10.1214/20-AAP1646
TypeArticle accepté pour publication ou publié
Journal nameAnnals of Applied Probability
Institute of Mathematical Statistics
MetadataShow full item record
Department of Mathematics [Burnaby] [SFU]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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,∞). 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 Poincaré Probab. Stat. 45 (2009) 734–753). We believe that our approach is simple enough to be applicable to many systems.
Subjects / Keywordsentropy dissipation; modified logarithmic Sobolev inequalities; Zero-range dynamics
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