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arXiv · 2601.16620

Generalized Logarithmic Sobolev Inequality by the JKO Scheme

Thibault Caillet·Fanch Coudreuse
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Abstract

Using a discrete Bakry-{\'E}mery method based on the JKO scheme, relying on the dissipation of entropy and Fisher information along a discrete flow, we establish new generalized logarithmic Sobolev inequality for log-concave measures of the form $e^{-V}$ under strict convexity assumptions on $V$ . We then show how this method recovers some well-known inequalities. This approach can be viewed as interpolating between the Bakry-{\'E}mery method and optimal transport techniques based on geodesic convexity.

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Thibault Caillet, Fanch Coudreuse. 2026-01-23. Generalized Logarithmic Sobolev Inequality by the JKO Scheme. https://arxiv.org/abs/2601.16620

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