We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.

翻译：我们为真正的对称和复杂的埃米提亚矩阵的最大精细的右尾小偏差估计值,这些矩阵的条目是独立的随机变量,具有单一的连接时间。 证据依靠绿色函数比较,长期与连续的内插矩阵流进行连续的相互比较。 在左边的尾巴中也得出了不那么精确的估计值。