Random Matrices with Equispaced External Source

被引：0
作者：
Tom Claeys
Dong Wang
机构：
[1] Université Catholique de Louvain,Department of Mathematics
[2] National University of Singapore,undefined
来源：
Communications in Mathematical Physics | 2014年 / 328卷
关键词：
External Source; Half Plane; Random Matrix; Equilibrium Measure; Jump Relation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends to infinity. We obtain strong asymptotics for the multiple orthogonal polynomials associated to these models, and as a consequence for the average characteristic polynomials. One feature of the multiple orthogonal polynomials analyzed in this paper is that the number of orthogonality weights of the polynomials grows with the degree. Nevertheless we are able to characterize them in terms of a pair of 2 × 1 vector-valued Riemann–Hilbert problems, and to perform an asymptotic analysis of the Riemann–Hilbert problems.
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页码：1023 / 1077
页数：54
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