Support convergence in the single ring theorem
Probability
2010-12-14 v1
Abstract
We study the eigenvalues of non-normal square matrices of the form A_n=U_nT_nV_n with U_n,V_n independent Haar distributed on the unitary group and T_n real diagonal. We show that when the empirical measure of the eigenvalues of T_n converges, and T_n satisfies some technical conditions, all these eigenvalues lie in a single ring.
Keywords
Cite
@article{arxiv.1012.2624,
title = {Support convergence in the single ring theorem},
author = {Alice Guionnet and Ofer Zeitouni},
journal= {arXiv preprint arXiv:1012.2624},
year = {2010}
}