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arXiv · 2410.06117

Improvement of Wu's logarithmic Sobolev inequality via the Poisson-F\"ollmer process

Shrey Aryan·Pablo López-Rivera·Yair Shenfeld
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Abstract

We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show that this approach leads to improvement of Wu's inequality under convexity assumptions.

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Shrey Aryan, Pablo López-Rivera, Yair Shenfeld. 2024-10-08. Improvement of Wu's logarithmic Sobolev inequality via the Poisson-F\"ollmer process. https://arxiv.org/abs/2410.06117

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