Calculus of Variations and Geometric Measure Theory

A. Figalli - A. Guionnet

Universality in several-matrix models via approximate transport maps

created by figalli on 16 Aug 2016
modified on 16 Dec 2016


Accepted Paper

Inserted: 16 aug 2016
Last Updated: 16 dec 2016

Journal: Acta Math.
Year: 2016


We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices (i.e., they are given by the sine-kernel in the bulk and the Tracy-Widom distribution at the edge), and we show averaged energy universality (i.e., universality for averages of $m$-points correlation functions around some energy level $E$ in the bulk). As a corollary, these results yield universality for self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.