LARGE DEVIATIONS FOR TOP EIGENVALUES OF β-JACOBI ENSEMBLES AT SCALING TEMPERATURES

被引：0
|
作者：
Lei, Liangzhen [1 ]
Ma, Yutao [2 ]
机构：
[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2023年 / 43卷 / 04期
关键词：
beta-Jacobi ensemble; large deviation; Wachter law; extremal eigenvalue; SPECTRAL MEASURES; LIMIT-THEOREMS;
D O I：
10.1007/s10473-023-0418-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let lambda = (lambda(1), center dot center dot center dot, lambda(n)) be beta-Jacobi ensembles with parameters p(1), p(2), n and beta, with beta varying with n. Set gamma = lim(n ->infinity) n/p1 and sigma = lim(n ->infinity) p1/p2. Suppose that lim(n ->infinity) log n/beta n = 0 and 0 <= sigma gamma < 1. We offer the large deviation for p1+p2/p1 max(1 <= i <= n) lambda i when gamma > 0 via the large deviation of the corresponding empirical measure and via a direct estimate, respectively, when gamma = 0
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页码：1767 / 1780
页数：14
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