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On optimal matching of Gaussian samples

Geometric functional analysis and applications November 13, 2017 - November 17, 2017

November 13, 2017 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Michel Ledoux (Institut de Mathématiques de Toulouse)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • optimal matching

  • Gaussian sample

  • optimal transport

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

2-Ledoux

Abstract

Optimal matching problems are random variational problems widely investigated in the mathematics and physics literature. We discuss here the optimal matching problem of an empirical measure on a sample of iid random variables to the common law in Kantorovich-Wasserstein distances, which is a classical topic in probability and statistics. Two-dimensional matching of uniform samples gave rise to deep results investigated from various view points (combinatorial, generic chaining). We study here the case of Gaussian samples, first in dimension one on the basis of explicit representations of Kantorovich metrics and a sharp analysis of more general log-concave distributions in terms of their isoperimetric profile (joint work with S. Bobkov), and then in dimension two (and higher) following the PDE and transportation approach recently put forward by L. Ambrosia, F. Stra and D. Trevisan.

Supplements
30088?type=thumb Ledoux Notes 627 KB application/pdf Download
Video/Audio Files

2-Ledoux

H.264 Video 2-Ledoux.mp4 98 MB video/mp4 rtsp://videos.msri.org/data/000/029/981/original/2-Ledoux.mp4 Download
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