论文标题
重新审视随机对称矩阵的奇异性
Singularity of random symmetric matrices revisited
论文作者
论文摘要
令$ m_n $从所有$ \ pm 1 $对称$ n \ times n $矩阵中均匀地绘制。我们表明，$ m_n $是单数的概率最多是$ \ exp（-c（n \ log n）^{1/2}）$，它代表了最近解决此问题的自然障碍。除了改善坎波斯，马托斯，莫里斯和莫里森的最著名的先前，$ \ exp（-c n^{1/2}）$上的奇异性概率外，我们的方法是不同的，而且更简单。
Let $M_n$ be drawn uniformly from all $\pm 1$ symmetric $n \times n$ matrices. We show that the probability that $M_n$ is singular is at most $\exp(-c(n\log n)^{1/2})$, which represents a natural barrier in recent approaches to this problem. In addition to improving on the best-known previous bound of Campos, Mattos, Morris and Morrison of $\exp(-c n^{1/2})$ on the singularity probability, our method is different and considerably simpler.
