Let Mn​ denote a random symmetric n by n matrix, whose upper diagonal
entries are iid Bernoulli random variables (which take value -1 and 1 with
probability 1/2). Improving the earlier result by Costello, Tao and Vu, we show
that Mn​ is non-singular with probability 1−O(n−C) for any positive
constant C. The proof uses an inverse Littlewood-Offord result for quadratic
forms, which is of interest of its own.Comment: Some minor corrections in Section 10 of v