Real Second Order Freeness and Haar Orthogonal Matrices
Operator Algebras
2015-06-11 v3 Probability
Abstract
We demonstrate the asymptotic real second order freeness of Haar distributed orthogonal matrices and an independent ensemble of random matrices. Our main result states that if we have two independent ensembles of random matrices with a real second order limit distribution and one of them is invariant under conjugation by an orthogonal matrix, then the two ensembles are asymptotically real second order free. This captures the known examples of asymptotic real second order freeness introduced by Redelmeier [R1, R2].
Cite
@article{arxiv.1210.6097,
title = {Real Second Order Freeness and Haar Orthogonal Matrices},
author = {James A. Mingo and Mihai Popa},
journal= {arXiv preprint arXiv:1210.6097},
year = {2015}
}
Comments
50 pages, revision has refreshed references and corrected typos