Optimal transport theory is an efficient tool to construct change of variables between probability densities. However, when it comes to the regularity of these maps, one cannot hope to obtain estimates that are uniform with respect to the dimension except in some very special cases (for instance, between uniformly logconcave densities). In random matrix theory the densities involved are pretty singular, so it seems hopeless to apply optimal transport theory in this context. However, ideas coming from optimal transport can still be used to construct approximate transport maps (i.e., maps which send a density onto another up to a small error) which enjoy regularity estimates that are uniform in the dimension. Such maps can then be used to show universality results for betaensembles.
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Transportation techniques for betaensembles
Research Group:
Prof. Alessio Figalli
Institution:
ETH, Zurich
Location:
A128
Schedule:
Thursday, June 1, 2017  14:00
Abstract:
Openings
Upcoming events

Zaher Hani
Effective dynamics of nonlinear Schroedinger equations on large domains  Part I
Tuesday, May 2, 2017 14:00 to 15:00

Zaher Hani
Effective dynamics of nonlinear Schroedinger equations on large domains  Part II
Wednesday, May 3, 2017 14:00 to 15:00

Rita Pardini
Mathematical Colloquium: Complex tori, abelian varieties and irregular projective varieties
Friday, May 12, 2017 16:00 to 17:00

Vieri Mastropietro
Mathematical Colloquium: Localization of interacting quantum particles with quasirandom disorder
Monday, May 22, 2017 16:00 to 17:00
Recent publications

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A. Michelangeli; A. Olgiati,GrossPitaevskii nonlinear dy...