Singularity of random symmetric matrices revisited
Abstract
Let $M_n$ be drawn uniformly from all $\pm 1$ symmetric $n \times n$ matrices. We show that the probability that $M_n$ is singular is at most $\exp(c(n\log n)^{1/2})$, which represents a natural barrier in recent approaches to this problem. In addition to improving on the bestknown previous bound of Campos, Mattos, Morris and Morrison of $\exp(c n^{1/2})$ on the singularity probability, our method is different and considerably simpler.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 arXiv:
 arXiv:2011.03013
 Bibcode:
 2020arXiv201103013C
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics
 EPrint:
 12 pages