R变换的渐近对数傅立叶解释
An asymptotic log-Fourier interpretation of the R-transform
摘要：
当一个矩阵的秩有限时，我们估计了球积分的渐近性。证明了它是由满秩矩阵的谱测度的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。这些渐近性也延伸到一个矩阵的秩为一，但复杂的特征值的情况下，与相应的球面积分的解析性的结果。
英文摘要：
We estimate the asymptotics of spherical integrals when the rank of one matrix is finite. 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.
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