1Departement of Mathematics [Austin] (The University of Texas at Austin, Mathematics Dept, RLM 8.100 2515 Speedway Stop C1200 Austin, Texas 78712-1202 - États-Unis)
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.
Type de document :
Article dans une revue
Acta Mathematica, Royal Swedish Academy of Sciences, Institut Mittag-Leffler, 2016, 217 (1), pp.115-159
https://hal-ens-lyon.archives-ouvertes.fr/ensl-01405141
Contributeur : Alice Guionnet
<>
Soumis le : mardi 29 novembre 2016 - 15:35:17
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31
Document(s) archivé(s) le : lundi 27 mars 2017 - 08:33:08
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〉
