Hermite-Pade approximations and multiple orthogonal polynomial ensembles

被引：37

作者：

Aptekarev, A. I. ^{[1
]}

Kuijlaars, A. B. J. ^{[2
]}

机构：

[1] Russian Acad Sci, Keldysh Inst Appl Math, Moscow 117901, Russia

[2] Katholieke Univ Leuven, Louvain, Belgium

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2011年 / 66卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

Hermite-Pade approximants; multiple orthogonal polynomials; weak and strong asymptotics; extremal equilibrium problems for a system of measures; matrix Riemann-Hilbert problem; Christoffel-Darboux formula; matrix model with an external source; non-intersecting paths; two-matrix model; DOUBLE SCALING LIMIT; GAUSSIAN RANDOM MATRICES; LARGE-N LIMIT; VECTOR EQUILIBRIUM PROBLEM; RIEMANN-HILBERT PROBLEMS; MARKOV-TYPE FUNCTIONS; SQUARED BESSEL PATHS; EXTERNAL SOURCE; BIORTHOGONAL POLYNOMIALS; STRONG ASYMPTOTICS;

D O I：

10.1070/RM2011v066n06ABEH004771

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with Hermite-Pade rational approximants of analytic functions and their connection with multiple orthogonal polynomial ensembles of random matrices. Results on the analytic theory of such approximants are discussed, namely, convergence and the distribution of the poles of the rational approximants, and a survey is given of results on the distribution of the eigenvalues of the corresponding random matrices and on various regimes of such distributions. An important notion used to describe and to prove these kinds of results is the equilibrium of vector potentials with interaction matrices. This notion was introduced by A. A. Gonchar and E. A. Rakhmanov in 1981.

引用

页码：1133 / 1199

页数：67

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