The paper focuses on the largest eigenvalues of theβ-Hermite ensemble and theβ-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated...The paper focuses on the largest eigenvalues of theβ-Hermite ensemble and theβ-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated by the complete convergence for partial sums of i.i.d, random variables, and the proofs depend on the small deviations for largest eigenvalues of the β ensembles and tail inequalities of the generalβ Tracy-Widom law.展开更多
基金Supported partly by the National Natural Science Foundation of China (Grant Nos. 11071213, 11101362)Zhejiang Provincial Natural Science Foundation of China (Grant No. R6090034)Research Fund for the Doctoral Program of Higher Education (Grant No. 20100101110001)
文摘The paper focuses on the largest eigenvalues of theβ-Hermite ensemble and theβ-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated by the complete convergence for partial sums of i.i.d, random variables, and the proofs depend on the small deviations for largest eigenvalues of the β ensembles and tail inequalities of the generalβ Tracy-Widom law.
