Universality in several-matrix models via approximate transport maps |
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Authors: | Alessio Figalli Alice Guionnet |
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Institution: | 1.Department of Mathematics,ETH Zürich,Zürich,Switzerland;2.Université de Lyon, école Normale Supérieure de Lyon, site Monod, UMPA UMR 5669 CNRS,Lyon Cedex 07,France |
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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), 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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