Transport maps for β-matrix models in the multi-cut regime

被引：5

作者：

Bekerman, Florent ^{[1
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

RANDOM MATRICES-THEORY AND APPLICATIONS | 2018年 / 7卷 / 01期

关键词：

Random matrices; beta-ensembles; central limit theorem; linear statistics; UNIVERSALITY; ENSEMBLES; SPECTRUM; EDGE;

D O I：

10.1142/S2010326317500137

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We use the transport methods develop in [F. Bekerman, A. Figalli and A. Guionnet, Transport maps for beta-matrix models and universality, Commun. Math. Phys. 338(2) (2013) 589-619] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for beta-matrix models in the multi-cut regime. We construct an approximate transport map inbetween two probability measures from the fixed filling fraction model discussed in [G. Borot, A. Guionnet and K. K. Kozlowski, Large-N asymptotic expansion for mean field models with coulomb gas interaction, Int. Math. Res. Not. (2015)] and deduce from it universality in the initial model.

引用

页数：36

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[2]

[Anonymous], 1999, COURANT LECT NOTES M

[3]

Bekerman F, 2015, COMMUN MATH PHYS, V338, P589, DOI 10.1007/s00220-015-2384-y

[4]

BenArous G, 1997, PROBAB THEORY REL, V108, P517

[5] Asymptotic Expansion of β Matrix Models in the One-cut Regime [J].