October 2021 Entropy dissipation estimates for inhomogeneous zero-range processes
Jonathan Hermon, Justin Salez
Author Affiliations +
Ann. Appl. Probab. 31(5): 2275-2283 (October 2021). DOI: 10.1214/20-AAP1646


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.

Funding Statement

The research of JH was supported by the EPSRC grant EP/L018896/1 and by an NSERC grant. The research of JS was supported in part by Institut Universitaire de France.


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Jonathan Hermon. Justin Salez. "Entropy dissipation estimates for inhomogeneous zero-range processes." Ann. Appl. Probab. 31 (5) 2275 - 2283, October 2021. https://doi.org/10.1214/20-AAP1646


Received: 1 November 2019; Revised: 1 September 2020; Published: October 2021
First available in Project Euclid: 29 October 2021

MathSciNet: MR4332696
zbMATH: 1476.60134
Digital Object Identifier: 10.1214/20-AAP1646

Primary: 60J27 , 60K35

Keywords: entropy dissipation , modified logarithmic Sobolev inequalities , Zero-range dynamics

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.31 • No. 5 • October 2021
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