On the Global Fluctuations of Block Gaussian Matrices
Probability
2017-11-21 v1 Operator Algebras
Abstract
In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy transform of these matrices, we introduce a matricial second-order conditional expectation and compute the matricial second-order Cauchy transform of a certain type of non-commutative random variables. As a by-product, using the linearization technique, we obtain the second-order Cauchy transform of non-commutative rational functions evaluated on selfadjoint Gaussian matrices.
Keywords
Cite
@article{arxiv.1711.07140,
title = {On the Global Fluctuations of Block Gaussian Matrices},
author = {Mario Diaz and James Mingo and Serban Belinschi},
journal= {arXiv preprint arXiv:1711.07140},
year = {2017}
}
Comments
32 pages, 9 figures