Bernstein-type inequality for a class of dependent random matrices

Marwa Banna, Florence Merlevède, Pierre Youssef

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Article number1650006
JournalRandom Matrices: Theory and Application
Volume5
Issue number2
DOIs
StatePublished - 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

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