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2016 Universality in several-matrix models via approximate transport maps
Alessio Figalli, Alice Guionnet
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Acta Math. 217(1): 81-176 (2016). DOI: 10.1007/s11511-016-0142-4

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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Alessio Figalli. Alice Guionnet. "Universality in several-matrix models via approximate transport maps." Acta Math. 217 (1) 81 - 176, 2016. https://doi.org/10.1007/s11511-016-0142-4

Information

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

zbMATH: 06697620
MathSciNet: MR3646880
Digital Object Identifier: 10.1007/s11511-016-0142-4

Rights: 2017 © Institut Mittag-Leffler

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Vol.217 • No. 1 • 2016
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