- Acta Math.
- Volume 217, Number 1 (2016), 81-176.
Universality in several-matrix models via approximate transport maps
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.
Acta Math., Volume 217, Number 1 (2016), 81-176.
Received: 30 July 2014
Revised: 16 August 2016
First available in Project Euclid: 22 February 2017
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2017 © Institut Mittag-Leffler
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