Limit Theorems and Large Deviations forβ-Jacobi Ensembles at Scaling Temperatures  

作　　者：Yu Tao MA 

机构地区：[1]School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第10期2054-2074,共21页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.12171038,11871008);985 Projects。

摘　　要：Letλ=(λ_(1),...,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβwhileβvarying with n.Setγ=lim_(n→∞)n/p_(1)andσ=lim_(n→∞)p_(1)/p_(2).In this paper,supposing lim_(n→∞)log_(n)/β_(n)=0,we prove that the empirical measures of different scaledλconverge weakly to a Wachter distribution,a Marchenko–Pastur law and a semicircle law corresponding toσγ>0,σ=0 orγ=0,respectively.We also offer a full large deviation principle with speedβn^(2)and a good rate function to precise the speed of these convergences.As an application,the strong law of large numbers for the extremal eigenvalues ofβ-Jacobi ensembles is obtained.

关 键 词：β-Jacobi ensemble large deviation principle semi-circle law Marchenko-Pastur law Wachter law 

分 类 号：O211.4[理学—概率论与数理统计]