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An asymptotic log-Fourier interpretation of the R-transform

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arxiv math/0406121 v3 pith:M3IVEOAS submitted 2004-06-07 math.PR hep-th

Alice Guionnet , Mylene Maida This is my paper · ORCID
classification math.PRhep-th
keywords matrixr-transformrankasymptoticsintegralssphericaladditiveanalyticity
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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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