Concentration inequalities for random matrix products

Matrix Concentration Inequalities

In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (formerly) challenging problems with a page or two of arithmetic. The aim of t...

\random" Random Matrix Products

Concentration Inequalities for Bounded Random Vectors

where z is a deterministic vector of the same dimension as Xn, the symbols “≤” and “≥” are used to denote the partial order relations between two vectors with the following notions: ∗The author is currently working with the Department of Electrical Engineering and Computer Sciences at Louisiana State University, Baton Rouge, LA 70803, USA, and the Department of Electrical Engineering at Souther...

Concentration inequalities for random fields via coupling

We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use information inequalities. When one has a uniform control on the coupling, this leads to exponential concentration inequalities. When such a uniform control is n...

Second-order Matrix Concentration Inequalities

Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies one of the sources of the dimensional term and exploits this insight to develop sharper matrix concentration inequalities. In particular, this analysis delive...