LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES  

作　　者：Naqi HUANG Yutao MA 黄娜琪;马宇韬(Faculty of Electrical Engineering,Mathematics and Computer Science,Delft University of Technology,Mekelweg 4,2628 CD Delft,The Netherlands;School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,Beijing 100875,China)

机构地区：[1]Faculty of Electrical Engineering,Mathematics and Computer Science,Delft University of Technology,Mekelweg 4,2628 CD Delft,The Netherlands [2]School of Mathematical Sciences&Laboratory of Mathematics and Complea Systems of Ministry of Education,Beijing Normal University,Beijing 100875,China

出　　处：《Acta Mathematica Scientia》2022年第5期2025-2039,共15页数学物理学报（B辑英文版）

基　　金：supported by NSFC(12171038,11871008).

摘　　要：We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles,focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles.For the central limit theorem of β-Laguerre ensembles,we follow the idea in[1]while giving a modified version for the generalized case.Then we use the total variation distance between the two sorts of ensembles to obtain the limiting behavior of β-Jacobi ensembles.

关 键 词：beta-ensembles largest and smallest eigenvalues central limit theorem total variationdistance 

分 类 号：O211.4[理学—概率论与数理统计]