Let A be a n by n matrix chosen uniformly at random among all symmetric matrices with entries in {-1,1}. In this talk we consider the following basic question: what is the probability that A is singular? I will discuss some recent progress on this problem and about how this problem is connected to understand other fundamental questions; the distribution of the least singular value and more generally the "bulk" spectrum of such matrices.
This is based work on joint work with Marcelo Campos, Matthew Jenssen and Marcus Michelen.
