Free products of large random matrices - a short review of recent developments
Mathematical Physics
2015-06-17 v2 Statistical Mechanics
math.MP
Abstract
We review methods to calculate eigenvalue distributions of products of large random matrices. We discuss a generalization of the law of free multiplication to non-Hermitian matrices and give a couple of examples illustrating how to use these methods in practice. In particular we calculate eigenvalue densities of products of Gaussian Hermitian and non-Hermitian matrices including combinations of GUE and Ginibre matrices.
Keywords
Cite
@article{arxiv.1309.2568,
title = {Free products of large random matrices - a short review of recent developments},
author = {Zdzislaw Burda},
journal= {arXiv preprint arXiv:1309.2568},
year = {2015}
}
Comments
Presented at the workshop: Inference, Computation, and Spin Glasses, Sapporo, July 28th-30th 2013