Gradient flows of the entropy for finite Markov chains
Seminar Room 2, Newton Institute Gatehouse
AbstractAt the end of the nineties, Jordan, Kinderlehrer, and Otto discovered a new interpretation of the heat equation in R^n, as the gradient flow of the entropy in the Wasserstein space of probability measures. In this talk, I will present a discrete counterpart to this result: given a reversible Markov kernel on a finite set, there exists a Riemannian metric on the space of probability densities, for which the law of the continuous time Markov chain evolves as the gradient flow of the entropy.
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