Calculus of Variations and Geometric Measure Theory

F. Bekermam - A. Figalli - A. Guionnet

Transport maps for $\beta$-matrix models and Universality

created by figalli on 30 Mar 2015


Accepted Paper

Inserted: 30 mar 2015
Last Updated: 30 mar 2015

Journal: Comm. Math. Phys.
Year: 2015


We construct approximate transport maps for non-critical $\beta$-matrix models, that is, maps so that the push forward of a non-critical $\beta$-matrix model with a given potential is a non-critical $\beta$-matrix model with another potential, up to a small error in the total variation distance. One of the main features of our construction is that these maps enjoy regularity estimates which are uniform in the dimension. In addition, we find a very useful asymptotic expansion for such maps which allow us to deduce that local statistics have the same asymptotic behavior for both models.