Operator-valued free multiplicative convolution: analytic subordination theory and applications to random matrix theory
Operator Algebras
2012-09-18 v1 Probability
Abstract
We give an explicit description, via analytic subordination, of free multiplicative convolution of operator-valued distributions. In particular, the subordination function is obtained from an iteration process. This algorithm is easily numerically implementable. We present two concrete applications of our method: the product of two free operator-valued semicircular elements and the calculation of the distribution of for scalar-valued and , which are free. Comparision between the solution obtained by our methods and simulations of random matrices shows excellent agreement.
Keywords
Cite
@article{arxiv.1209.3508,
title = {Operator-valued free multiplicative convolution: analytic subordination theory and applications to random matrix theory},
author = {Serban T. Belinschi and Roland Speicher and John Treilhard and Carlos Vargas},
journal= {arXiv preprint arXiv:1209.3508},
year = {2012}
}