The Poisson transport map
Probability
2025-02-07 v2
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.
Cite
@article{arxiv.2407.02359,
title = {The Poisson transport map},
author = {Pablo López-Rivera and Yair Shenfeld},
journal= {arXiv preprint arXiv:2407.02359},
year = {2025}
}