Random Matrices with Equispaced External Source
Random Matrices with Equispaced External Source
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DOI：
10.1007/s00220-014-1988-y
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发表时间：
2012-12
影响因子：
2.4
通讯作者：
T. Claeys;Dong Wang
中科院分区：
文献类型：
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作者：
T. Claeys;Dong Wang
本文研究了具有等阶特征值的外源矩阵和具有当维数趋于无穷时在单个区间上支持特征值的极限平均密度的外场的厄米随机矩阵模型。我们获得了与这些模型相关的多个正交多项式的强渐近性，并作为平均特征多项式的结果。本文所分析的多重正交多项式的一个特征是多项式的正交权值的个数随着阶数的增加而增加。然而，我们能够用一对2 × 1向量值黎曼-希尔伯特问题来描述它们，并对黎曼-希尔伯特问题进行渐近分析。
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.