Painlev, Kernels in Hermitian Matrix Models

被引：8

作者：

Duits, Maurice ^{[1
]}

机构：

[1] Royal Inst Technol KTH, Dept Math, S-10044 Stockholm, Sweden

来源：

CONSTRUCTIVE APPROXIMATION | 2014年 / 39卷 / 01期

关键词：

Hermitian matrix models; Eigenvalue distribution; Correlation kernel; Critical phenomena; Painleve transcendents; Biorthogonal polynomials; Riemann-Hilbert problems; DOUBLE SCALING LIMIT; GAUSSIAN RANDOM MATRICES; RIEMANN-HILBERT PROBLEM; LARGE N LIMIT; BIORTHOGONAL POLYNOMIALS; ORTHOGONAL POLYNOMIALS; EXTERNAL SOURCE; 2-MATRIX MODEL; UNIVERSALITY; ASYMPTOTICS;

D O I：

10.1007/s00365-013-9201-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

After reviewing the Hermitian one-matrix model, we will give a brief introduction to the Hermitian two-matrix model and present a summary of some recent results on the asymptotic behavior of the two-matrix model with a quartic potential. In particular, we will discuss a limiting kernel in the quartic/quadratic case that is constructed out of a 4x4 Riemann-Hilbert problem related to the Painlev, II equation. Also an open problem will be presented.

引用

页码：173 / 196

页数：24

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