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arXiv · 2407.02359

The Poisson transport map

Pablo López-Rivera·Yair Shenfeld
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Abstract

We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities using transport maps in discrete settings, and allows us to deduce a number of functional inequalities for ultra-log-concave measures. In particular, we provide the currently best known constant in modified logarithmic Sobolev inequalities for ultra-log-concave measures.

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Pablo López-Rivera, Yair Shenfeld. 2024-07-02. The Poisson transport map. https://arxiv.org/abs/2407.02359

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