The Poisson transport map

Fuente: arXiv
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Main Authors: López-Rivera, Pablo, Shenfeld, Yair
Format: Preprint
Published: 2024
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author López-Rivera, Pablo
Shenfeld, Yair
author_facet López-Rivera, Pablo
Shenfeld, Yair
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_02359
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Poisson transport map
López-Rivera, Pablo
Shenfeld, Yair
Probability
39B62, 60G55, 60H07
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.
title The Poisson transport map
topic Probability
39B62, 60G55, 60H07
url https://arxiv.org/abs/2407.02359