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

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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≤n.In 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,respectively.This recovers some well-known results.Moreover,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 convergence.The minimizer of I_(γ) is a modified Marchenko-Pastur law forγ∈(0,1]and the semicircle law forγ=0.
作者 Yu Tao MA
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第7期1271-1288,共18页 数学学报(英文版)
基金 Supported by NSFC(Grant Nos.12171038,11871008) the National Key R&D Program of China(Grant No.2020YFA0712900) 985 Projects。
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