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
收藏
页码：173 / 196
页数：24
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