An asymptotic log-Fourier interpretation of the R-transform
Probability
2007-05-23 v3 High Energy Physics - Theory
Abstract
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.
Cite
@article{arxiv.math/0406121,
title = {An asymptotic log-Fourier interpretation of the R-transform},
author = {Alice Guionnet and Mylene Maida},
journal= {arXiv preprint arXiv:math/0406121},
year = {2007}
}
Comments
Revised version : the proof for the full asymptotics in rank one has been corrected and a bit shortened. An appendix was added