The singularity probability of a random symmetric matrix is exponentially small

Seminar series

Date

Tue, 16 Nov 2021
14:00

Location

Speaker

Matthew Jenssen

Let $A$ be drawn uniformly at random from the set of all $n \times n$ symmetric matrices with entries in $\{-1,1\}$ . We show that $A$ is singular with probability at most $e^{-cn}$ for some absolute constant $c>0$ , thereby resolving a well-known conjecture. This is joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe.