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Zbl 1181.60142
Caputo, Pietro; Pra, Paolo Dai; Posta, Gustavo
Convex entropy decay via the Bochner-Bakry-Emery approach. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 45, No. 3, 734-753 (2009). ISSN 0246-0203

Summary: We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli-Laplace models. For these two models, known results were limited to the homogeneous case, and obtained via the martingale approach, whose applicability to inhomogeneous models is still unclear.

MSC 2000:: *60K35 Interacting random processes
39B62 Systems of functional equations
60J80 Branching processes

Keywords: entropy decay; modified logarithmic Sobolev inequality; stochastic particle systems

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