Asymptotic Freeness for Rectangular Random Matrices and Large Deviations for Sample Covariance Matrices With Sub-Gaussian Tails
Probability
2015-05-22 v1
Abstract
We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices having the same type of entries [7]. To this aim, we need to establish an asymptotic freeness result for rectangular free convolution, more precisely, we give a bound in the subordination formula for information-plus-noise matrices.
Cite
@article{arxiv.1505.05733,
title = {Asymptotic Freeness for Rectangular Random Matrices and Large Deviations for Sample Covariance Matrices With Sub-Gaussian Tails},
author = {Benjamin Groux},
journal= {arXiv preprint arXiv:1505.05733},
year = {2015}
}