Work

Non-asymptotic Theory of Random Matrices: Extreme Singular Values

Year: 2011

Type: conference-paper

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).

Source: International Congress of Mathematicians (ICM)

DOI: 10.1142/9789814324359_0111

Authors: Mark Rudelson, Roman Vershynin

Institutions: University of Missouri, University of Michigan

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: FRG: Collaborative Research: Fourier analytic and probabilistic methods in geometric functional analysis and convexity, FRG: Collaborative Research: Fourier analytic and probabilistic methods in geometric functional analysis and convexity