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arXiv · 1101.3074

Inverse Littlewood-Offord problems and The Singularity of Random Symmetric Matrices

Hoi H. Nguyen
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Abstract

Let $M_n$ 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 $M_n$ 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.

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Hoi H. Nguyen. 2012-12-31. Inverse Littlewood-Offord problems and The Singularity of Random Symmetric Matrices. https://doi.org/10.1215/00127094-1548344

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