Bernstein type inequality for a class of dependent random matrices
Probability
2018-07-19 v1
Abstract
In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix setting of the Bernstein-type inequality obtained by Merlev\`ede et al. (2009) in the context of real-valued bounded random variables that are geometrically absolutely regular. The proofs rely on decoupling the Laplace transform of a sum on a Cantor-like set of random matrices.
Cite
@article{arxiv.1504.05834,
title = {Bernstein type inequality for a class of dependent random matrices},
author = {Marwa Banna and Florence Merlevède and Pierre Youssef},
journal= {arXiv preprint arXiv:1504.05834},
year = {2018}
}
Comments
22 pages