Andrei Deneanu, Yale University

Abstract

We consider a random nxn matrix, M_n, whose entries are independent and identically distributed (i.i.d.) Rademacher random variables (taking values {-1,1} with probability 1/2) and prove 2^{-(0.5+o(1))n^2} <=P (M_n is normal) <= 2^{-(0.302+o(1))n^{2}}. We conjecture that the lower bound is sharp.