中文摘要：

对于相当广泛的边界函数和拟权函数,利用β-Hermite随机矩阵最大特征值的弱收敛定理、小偏差结论及广义βTracy-Wisdom分布的尾概率不等式,得到了其最大特征值的矩完全收敛性的精确渐近性的一般形式.

英文摘要：

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.