Growth estimates on optimal transport maps via concentration inequalities

Fuente: arXiv
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Main Author: Fathi, Max
Format: Preprint
Published: 2024
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author Fathi, Max
author_facet Fathi, Max
contents We give an alternative proof and some extensions of results of Carlier, Figalli and Santambrogio on polynomial upper bounds on the Brenier map between probability measures under various conditions on the densities. The proofs are based on the monotonicity of the map and various concentration inequalities, as already used by Colombo and Fathi to prove quadratic growth for transport maps from the standard Gaussian onto log-concave measures.
format Preprint
id arxiv_https___arxiv_org_abs_2407_11951
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Growth estimates on optimal transport maps via concentration inequalities
Fathi, Max
Analysis of PDEs
Functional Analysis
Optimization and Control
Probability
We give an alternative proof and some extensions of results of Carlier, Figalli and Santambrogio on polynomial upper bounds on the Brenier map between probability measures under various conditions on the densities. The proofs are based on the monotonicity of the map and various concentration inequalities, as already used by Colombo and Fathi to prove quadratic growth for transport maps from the standard Gaussian onto log-concave measures.
title Growth estimates on optimal transport maps via concentration inequalities
topic Analysis of PDEs
Functional Analysis
Optimization and Control
Probability
url https://arxiv.org/abs/2407.11951