## 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 Merlevède et al. [Bernstein inequality and moderate deviations under strong mixing conditions, in High Dimensional Probability V: The Luminy Volume, Institute of Mathematical Statistics Collection, Vol. 5 (Institute of Mathematical Statistics, Beachwood, OH, 2009), pp. 273-292.] 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.

Original language | English (US) |
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Article number | 1650006 |

Journal | Random Matrices: Theory and Application |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2016 |

## Keywords

- Bernstein inequality
- Random matrices
- absolute regularity
- deviation inequality
- β -mixing coefficients

## ASJC Scopus subject areas

- Algebra and Number Theory
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Discrete Mathematics and Combinatorics