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2015 Eigenvalue distribution of optimal transportation
Bo’az Klartag, Alexander Kolesnikov
Anal. PDE 8(1): 33-55 (2015). DOI: 10.2140/apde.2015.8.33

Abstract

We investigate the Brenier map Φ between the uniform measures on two convex domains in n, or, more generally, between two log-concave probability measures on n. We show that the eigenvalues of the Hessian matrix D2Φ exhibit concentration properties on a multiplicative scale, regardless of the choice of the two measures or the dimension n.

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Bo’az Klartag. Alexander Kolesnikov. "Eigenvalue distribution of optimal transportation." Anal. PDE 8 (1) 33 - 55, 2015. https://doi.org/10.2140/apde.2015.8.33

Information

Received: 13 February 2014; Accepted: 2 December 2014; Published: 2015
First available in Project Euclid: 28 November 2017

zbMATH: 1325.35130
MathSciNet: MR3336921
Digital Object Identifier: 10.2140/apde.2015.8.33

Subjects:
Primary: 35J96

Rights: Copyright © 2015 Mathematical Sciences Publishers

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