Speaker: Vishesh Jain (UC Berkeley)

Title: Singularity of Discrete Random Matrices
Abstract: Let $\xi$ be a discrete random variable, and let $M_n$ be an $n\times n$ random matrix whose entries are independent copies of $\xi$. One of the most basic questions in the non-asymptotic theory of random matrices is to estimate the probability that $M_n$ is not invertible. I will discuss recent progress towards confirming the widely held belief that this probability is dominated by the event that $M_n$ has a zero row or column, or that two of its rows or columns are equal (up to a sign). Based on joint work with Ashwin Sah (MIT) and Mehtaab Sawhney (MIT).