Convexity of mutual information along the heat flow

ISIT, pp. 1615-1619, 2018.

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Abstract:

We study the convexity of mutual information along the evolution of the heat equation. We prove that if the initial distribution is log-concave, then mutual information is always a convex function of time. We also prove that if the initial distribution is either bounded, or has finite fourth moment and Fisher information, then mutual info...More

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