Non-asymptotic Theory of Random Matrices: Extreme Singular Values

Mark Rudelson, Roman Vershynin

Type: Article

Publication Date: 2011-04-15

Citations: 190

DOI: https://doi.org/10.1142/9789814324359_0111

Abstract

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices with independent entries. We focus on recently developed geometric methods for estimating the hard edge of random matrices (the smallest singular value).

Locations

arXiv (Cornell University) - View - PDF
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010) - View

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