# LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS

@article{Diaconis1996LOGARITHMICSI, title={LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS}, author={Persi Diaconis and Laurent Saloff-Coste}, journal={Annals of Applied Probability}, year={1996}, volume={6}, pages={695-750} }

This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous time. Some aspects of the theory simplify considerably with finite state spaces and we are able to give a self-contained development. Examples of applications include the study of a Metropolis chain…

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