UNIVERSALITY IN SEVERAL-MATRIX MODELS VIA APPROXIMATE TRANSPORT MAPS

A Figalli (1) , A Guionnet (2, 3)

1 Departement of Mathematics [Austin]
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 Department of Mathematics [MIT]

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.

Domains: Mathematics [math]; Probability [math.PR]

A Figalli, A Guionnet. UNIVERSALITY IN SEVERAL-MATRIX MODELS VIA APPROXIMATE TRANSPORT MAPS. Acta Mathematica, 2016, 217 (1), pp.115-159. ⟨ensl-01405141⟩