UNIVERSALITY IN SEVERAL-MATRIX MODELS VIA APPROXIMATE TRANSPORT MAPS

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), 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.
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Submitted on : Tuesday, November 29, 2016 - 3:35:17 PM
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A Figalli, A Guionnet. UNIVERSALITY IN SEVERAL-MATRIX MODELS VIA APPROXIMATE TRANSPORT MAPS. Acta Mathematica, Royal Swedish Academy of Sciences, Institut Mittag-Leffler, 2016, 217 (1), pp.115-159. ⟨ensl-01405141⟩

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