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