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A Bernstein inequality for dependent random matrices

Banff International Research Station for Mathematical Innovation and Discovery

The classical Bernstein inequality shows that the sum of bounded independent random variables is concentrated around its expectation in terms of the variance of the sum’s increments. In this talk, we are interested by a Bernstein-type inequality for the largest eigenvalue of the sum of dependant Hermitian random matrices with bounded operator norm. In the case where the matrices are independent, the matrix version of the Bernstein inequality was due to Ahlswede et Winter (2002) and was then improved by Tropp (2012). In this talk, we shall see how to relax the independence condition and extend this inequality to a class of dependent matrices. We shall also shed light on some difficulties arising from the non-commutative and dependence setting. (joint work with F. Merlevède and P. Youssef)

Mathematics; Functional analysis; Probability theory and stochastic processes; Operator theory/algebras

video/mp4

Author affiliation: Saarland University

2017-05-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61639

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/