# Singularity of random symmetric matrices revisited

@article{Campos2020SingularityOR, title={Singularity of random symmetric matrices revisited}, author={Marcelo Campos and Matthew Jenssen and Marcus Michelen and Julian Sahasrabudhe}, journal={arXiv: Probability}, year={2020} }

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 best-known 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.

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