Inverse Littlewood-offord Problems and the Singularity of Random Symmetric Matrices
نویسنده
چکیده
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 [4], we show that Mn is nonsingular 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.
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