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Gradient flows of the entropy for finite Markov chains

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Discrete Analysis

At 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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