80 citations · 602 across the 56 of their papers we have counts for
16 papers · 1 filter
Non-asymptotic theory of random matrices: extreme singular values
Mark Rudelson, Roman Vershynin
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 applica…
Random sets of isomorphism of linear operators on Hilbert space
Roman Vershynin
This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator on a Hilbert space with an orthogonal basis, we define the iso…
Sampling from large matrices: an approach through geometric functional analysis
Mark Rudelson, Roman Vershynin
We study random submatrices of a large matrix A. We show how to approximately compute A from its random submatrix of the smallest possible size O(r log r) with a small error in the…
Geometric approach to error correcting codes and reconstruction of signals
Mark Rudelson, Roman Vershynin
We develop an approach through geometric functional analysis to error correcting codes and to reconstruction of signals from few linear measurements. An error correcting code encod…
Small ball probability and Dvoretzky theorem
Bo'az Klartag, Roman Vershynin
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldev…
Frame expansions with erasures: an approach through the non-commutative operator theory
Roman Vershynin
In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using ove…