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Inverse Littlewood–Offord problems and the singularity of random symmetric matrices

Inverse Littlewood–Offord problems and the singularity of random symmetric matrices

Let Mn denote a random symmetric (n×n)-matrix whose upper diagonal entries are independent and identically distributed Bernoulli random variables (which take value −1 and 1 with probability 1/2). Improving the earlier result by Costello, Tao, and Vu [4], we show that Mn is nonsingular with probability 1−O(n−C) for any positive …