Exponential convergence rate in entropy

Abstract

The exponential convergence rate in entroy is studied for symmetric forms, with a special attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.

Keywords

Exponential convergence rate / spectral gap / logarithmic Sobolev constant / symmetric form / Markov chain

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