Acta Mathematica

Universality in several-matrix models via approximate transport maps

Alessio Figalli and Alice Guionnet

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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.

Article information

Source
Acta Math., Volume 217, Number 1 (2016), 81-176.

Dates
Received: 30 July 2014
Revised: 16 August 2016
First available in Project Euclid: 22 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1487789799

Digital Object Identifier
doi:10.1007/s11511-016-0142-4

Mathematical Reviews number (MathSciNet)
MR3646880

Zentralblatt MATH identifier
06697620

Rights
2017 © Institut Mittag-Leffler

Citation

Figalli, Alessio; Guionnet, Alice. Universality in several-matrix models via approximate transport maps. Acta Math. 217 (2016), no. 1, 81--176. doi:10.1007/s11511-016-0142-4. https://projecteuclid.org/euclid.acta/1487789799


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