Eigenvalue distribution of optimal transportation

Bo'Az B. Klartag; Alexander V. Kolesnikov

doi:10.2140/apde.2015.8.33

Eigenvalue distribution of optimal transportation

Bo'Az B. Klartag, Alexander V. Kolesnikov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the Brenier map del Phi between the uniform measures on two convex domains in R-n, or, more generally, between two log-concave probability measures on R-n. We show that the eigenvalues of the Hessian matrix D-2 Phi exhibit concentration properties on a multiplicative scale, regardless of the choice of the two measures or the dimension n.

Original language	English
Pages (from-to)	33-55
Number of pages	23
Journal	Analysis and PDE
Volume	8
Issue number	1
DOIs	https://doi.org/10.2140/apde.2015.8.33
State	Published - 15 Apr 2015

Keywords

Log-concave measures
Transportation of measure

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Numerical Analysis

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10.2140/apde.2015.8.33

http://arxiv.org/abs/1402.2636License: Other

Cite this

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Eigenvalue distribution of optimal transportation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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