Unified Limits and Large Deviation Principles forβ-Laguerre Ensembles in Global Regime

作     者：Yu Tao MA Yu Tao MA

作者机构：School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of EducationBeijing Normal UniversityBeijing 100875China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第7期

页      面：1271-1288页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by NSFC(Grant Nos.12171038,11871008) the National Key R&D Program of China(Grant No.2020YFA0712900) 985 Projects 

主　　题：β-Laguerre ensemble large deviation principle empirical measure semicircular law Marchenko–Pastur law 

摘      要：Let(λ_(1),...,λ_(n)) be β-Laguerre ensembles with parametersβ,p,n and μ_(n):=1/n∑^(n)_(i=1)δ_(Xi) with for 1≤i≤*** this paper,asβvaries and satisfies lim_(n→∞)log n/βn=0,we offer a modified Marchenko-Pastur,law or semicircle law as the weak limits for the sequence μ_(n) when lim_(n→∞)n/p=γ∈(0,1]or lim_(n→∞)n/p=0,*** recovers some well-known ***,we give a full large deviation principle of μ_(n) with speed βn^(2) and good rate function I_(γ) under the same condition to characterize the speed of the *** minimizer of I_(γ) is a modified Marchenko-Pastur law forγ∈(0,1]and the semicircle law forγ=0.