On the singularity probability of random Bernoulli matrices
Combinatorics
2008-08-06 v2
Abstract
Let be a large integer and be a random by matrix whose entries are i.i.d. Bernoulli random variables (each entry is with probability 1/2). We show that the probability that is singular is at most , improving an earlier estimate of Kahn, Koml\'os and Szemer\'edi, as well as earlier work by the authors. The key new ingredient is the applications of Freiman type inverse theorems and other tools from additive combinatorics.
Cite
@article{arxiv.math/0501313,
title = {On the singularity probability of random Bernoulli matrices},
author = {Terence Tao and Van Vu},
journal= {arXiv preprint arXiv:math/0501313},
year = {2008}
}
Comments
30 pages, no figures. This is the final version