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A. Jüngel, W. Yue:
"Discrete Beckner inequalities via the bochner-Bakry-Emery approach for Markov chains";
in: "ASC Report 36/2015", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, S. 1 - 26.

Discrete Beckner inequalities, which interpolate between the modified loga-rithmic Sobolev inequality and the Poincare´ inequality, are derived for time-continuous Markov chains on countable state spaces. The proof is based on the Bakry-Emery ap-proach and on discrete Bochner-type inequalities established by Caputo, Dai Pra, and Posta and recently extended by Fathi and Maas. The abstract result is applied to several Markov chains, including birth-death processes, zero-range processes, Bernoulli-Laplace models, and random transportation models, and to a finite-volume discretization of a one-dimensional Fokker-Planck equation, applying results by Mielke.

Time-continuous Markov chain, functional inequality, entropy decay, discrete, Time-continuous Markov chain, functional inequality, entropy decay

http://www.asc.tuwien.ac.at/preprint/2015/asc36x2015.pdf