Introduction to the non-asymptotic analysis of random matrices

Orateur:
VERSHYNIN Roman
Localisation: Université du Michigan, États-Unis
Type: Cours doctoraux
Site: Hors LAMA , IHP
Salle:
Amphithéâtre Darboux
Date de début:
21/06/2011 - 09:00
Date de fin:
21/06/2011 - 09:00

This is a mini-course on basic non-asymptotic methods and concepts in random matrix theory. We will develop several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis in the 1970-2000's. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. Two applications will be discussed: for the problem of estimating covariance matrices in statistics, and for validating probabilistic constructions of measurement matrices in compressed sensing.