Acta Mathematica

, Volume 217, Issue 1, pp 81–176 | Cite as

Universality in several-matrix models via approximate transport maps

  • Alessio Figalli
  • Alice Guionnet


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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© Institut Mittag-Leffler 2017

Authors and Affiliations

  1. 1.Department of MathematicsETH ZürichZürichSwitzerland
  2. 2.Université de Lyon, École Normale Supérieure de Lyon, site Monod, UMPA UMR 5669 CNRSLyon Cedex 07France

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