A Fourier view on the R-transform and related asymptotics of spherical integrals
A Fourier view on the R-transform and related asymptotics of spherical integrals
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DOI：
10.1016/j.jfa.2004.09.015
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发表时间：
2005-05-15
影响因子：
1.7
通讯作者：
Maïda, M
中科院分区：
文献类型：
--
作者：
Guionnet, A;Maïda, M
当一个矩阵的秩远小于它的维时，我们估计了实对称或厄米特矩阵的球积分的渐近性。我们证明了它是用满秩矩阵谱测度的R变换给出的，并给出了R变换在自由卷积下是可加的一个新的证明。这些渐近性也推广到一个矩阵具有一阶复本征值的情况，这一结果与相应的球面积分的解析性有关。(C)2004 Elsevier Inc.保留所有权利。
We estimate the asymptotics of spherical integrals of real symmetric or Hermitian matrices when the rank of one matrix is much smaller than its dimension. We show that it is given in terms of the R-transform of the spectral measure of the full rank matrix and give a new proof of the fact that the R-transform is additive under free convolution. These asymptotics also extend to the case where one matrix has rank one but complex eigenvalue, a result related with the analyticity of the corresponding spherical integrals. (c) 2004 Elsevier Inc. All rights reserved.