论文标题
在随机对称矩阵的永久性上
On the permanent of a random symmetric matrix
论文作者
论文摘要
令$ m_ {n} $表示随机对称$ n \ times n $矩阵，其对角线的条目为i.i.d. Rademacher随机变量（将值$ \ pm 1 $带有概率$ 1/2 $）。解决vu的猜想，我们证明$ m_ {n} $的永久性具有幅度$ n^{n/2+o（n）} $，概率$ 1-o（1）$。我们的结果也可以扩展到更一般的随机矩阵模型。
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.
