Gradient flows of the entropy for finite Markov chains

  title={Gradient flows of the entropy for finite Markov chains},
  author={Jan Maas},
  journal={Journal of Functional Analysis},
  • Jan Maas
  • Published 2011
  • Mathematics
  • Journal of Functional Analysis
  • Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wasserstein gradient flow interpretation of the heat flow in Rn by Jordan, Kinderlehrer and Otto (1998). The metric W is similar to, but different from, the L2-Wasserstein metric, and is… CONTINUE READING
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