Discrete Beckner Inequalities via a Bochner-Bakry-Emery Method for Markov Chains

Wen Yue (Technology University of Vienna)

Frank Adams 2,

Beckner inequalities, which interpolate between the logarithmic Sobolev Inequalities and Poincare inequalities, are derived in the context of Markov chains. The proof is based on the Bakry-Emery method and the use of discrete Bochner-type inequalities. We apply our result to several Markov chains including Birth-Death process, Zero-Range process, Bernoulli-Laplace models and Random Transposition models and thus get the exponential convergence rates of the ''distributions'' of these Markov chains to their invariant measures.)

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