Polynomial bounds for large Bernoulli sections of $\ell_1^N$
Functional Analysis
2007-08-14 v2 Mathematical Physics
Metric Geometry
math.MP
Abstract
We prove a quantitative version of the bound on the smallest singular value of a Bernoulli covariance matrix (due to Bai and Yin). Then we use this bound, together with several recent developments, to show that the distance from a random (1-delta) n - dimensional section of ell_1^n, realised as an image of a sign matrix, to an Euclidean ball is polynomial in 1/delta (and independent of n), with high probability.
Keywords
Cite
@article{arxiv.math/0601369,
title = {Polynomial bounds for large Bernoulli sections of $\ell_1^N$},
author = {Shiri Artstein-Avidan and Omer Friedland and Vitali Milman and Sasha Sodin},
journal= {arXiv preprint arXiv:math/0601369},
year = {2007}
}
Comments
22 pages