Universality in several-matrix models via approximate transport maps

Alessio Figalli; Alice Guionnet

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arXiv · 1407.2759

Universality in several-matrix models via approximate transport maps

Alessio Figalli·Alice Guionnet

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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.

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Alessio Figalli, Alice Guionnet. 2014-07-10. Universality in several-matrix models via approximate transport maps. https://arxiv.org/abs/1407.2759

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