Universality in several-matrix models via approximate transport maps
Probability
2016-03-21 v4
Abstract
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. Moreover, we prove universality for the local statistics of eigenvalues of self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.
Cite
@article{arxiv.1407.2759,
title = {Universality in several-matrix models via approximate transport maps},
author = {Alessio Figalli and Alice Guionnet},
journal= {arXiv preprint arXiv:1407.2759},
year = {2016}
}