关键词: 广义β-Tracy-Wisdom分布, 精确渐近性, 最大特征值, 矩完全收敛性, 一般形式

Abstract: For a fairly wide range of boundary function and quasi weight function, the author obtained a general form of precise asymptotics in complete moment convergence for the largest eigenvalue by using the weak convergence theorem and the small deviation conclusion for largest eigenvalue of β-Hermite random matrix and tail probability inequality of the general β-Tracy-Wisdom distribution.

Key words: general β-Tracy-Wisdom distribution, precise asymptotics,  largest eigenvalue, complete moment convergence, general form