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Limit Theorems for β-Laguerre and β-Jacobi Ensembles

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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.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    Naqi Huang  (黄娜琪)

  2. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing, 100875, China

    Yutao Ma  (马宇韬)

Authors
  1. Naqi Huang  (黄娜琪)
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  2. Yutao Ma  (马宇韬)
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Corresponding author

Correspondence to Yutao Ma  (马宇韬).

Additional information

Yutao Ma was supported by NSFC (12171038, 11871008).

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Huang, N., Ma, Y. Limit Theorems for β-Laguerre and β-Jacobi Ensembles. Acta Math Sci 42, 2025–2039 (2022). https://doi.org/10.1007/s10473-022-0517-x

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  • DOI: https://doi.org/10.1007/s10473-022-0517-x

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