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On the permanent of a random symmetric matrix
Matthew Kwan, Lisa Sauermann · 2020-10-18 · via math.PR updates on arXiv.org

Let $M_{n}$ denote a random symmetric $n\times n$ matrix, whose entries on and above the diagonal are i.i.d. Rademacher random variables (taking values $\pm 1$ with probability $1/2$ each). Resolving a conjecture of Vu, we prove that the permanent of $M_{n}$ has magnitude $n^{n/2+o(n)}$ with probability $1-o(1)$. Our result can also be extended to more general models of random matrices.

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