Convexity and regularity properties for entropic interpolations

Luigia Ripani

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arXiv · 1711.08230

Convexity and regularity properties for entropic interpolations

Luigia Ripani

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Abstract

In this paper we prove a convexity property of the relative entropy along entropic interpolations (solutions of the Schr\"odinger problem), and a regularity property of the entropic cost along the heat flow. Then we derive a dimensional EVI inequality and a contraction property for the entropic cost along the heat flow. As a consequence, we recover the equivalent results in the Wasserstein space, proved by Erbar, Kuwada and Sturm.

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Luigia Ripani. 2017-11-22. Convexity and regularity properties for entropic interpolations. https://arxiv.org/abs/1711.08230

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