English

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.

Keywords

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

R2 v1 2026-06-22T09:20:34.270Z