LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES

doi:10.1007/s10473-022-0517-x

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 2025-2039.doi: 10.1007/s10473-022-0517-x

• 论文 • 上一篇

LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES

Naqi HUANG¹, Yutao MA²

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 Complex Systems of Ministry of Education, Beijing Normal University, Beijing, 100875, China

收稿日期:2020-12-01 修回日期:2022-05-20 发布日期:2022-11-02
通讯作者: Yutao Ma,E-mail:mayt@bnu.edu.cn E-mail:mayt@bnu.edu.cn
基金资助:
Yutao Ma was supported by NSFC (12171038, 11871008).

LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES

Naqi HUANG¹, Yutao MA²

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 Complex Systems of Ministry of Education, Beijing Normal University, Beijing, 100875, China

Received:2020-12-01 Revised:2022-05-20 Published:2022-11-02
Contact: Yutao Ma,E-mail:mayt@bnu.edu.cn E-mail:mayt@bnu.edu.cn
Supported by:
Yutao Ma was supported by NSFC (12171038, 11871008).

摘要/Abstract

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 variation distance

Abstract: 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.

Key words: beta-ensembles, largest and smallest eigenvalues, central limit theorem, total variation distance

中图分类号:

15B52

Naqi HUANG, Yutao MA. LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES[J]. 数学物理学报(英文版), 2022, 42(5): 2025-2039.

Naqi HUANG, Yutao MA. LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES[J]. Acta mathematica scientia,Series B, 2022, 42(5): 2025-2039.

参考文献

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LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES

LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES

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