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arXiv · 1504.05834

Bernstein type inequality for a class of dependent random matrices

Marwa Banna·Florence Merlevède·Pierre Youssef
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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. (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.

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Marwa Banna, Florence Merlevède, Pierre Youssef. 2015-04-22. Bernstein type inequality for a class of dependent random matrices. https://doi.org/10.1142/s2010326316500064

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