On the singularity probability of discrete random matrices
Combinatorics
2009-05-05 v1
Abstract
Let be an by random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that is singular is at most , improving on the previous best upper bound of proven by Tao and Vu in arXiv:math/0501313v2. This paper follows a similar approach to the Tao and Vu result, including using a variant of their structure theorem. We also extend this type of exponential upper bound on the probability that a random matrix is singular to a large class of discrete random matrices taking values in the complex numbers, where the entries are independent but are not necessarily identically distributed.
Keywords
Cite
@article{arxiv.0905.0461,
title = {On the singularity probability of discrete random matrices},
author = {Jean Bourgain and Van Vu and Philip Matchett Wood},
journal= {arXiv preprint arXiv:0905.0461},
year = {2009}
}
Comments
45 pages, two figures