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Limit Theorems for β-Laguerre and β-Jacobi Ensembles

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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Correspondence to Yutao Ma.

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

Key words

  • beta-ensembles
  • largest and smallest eigenvalues
  • central limit theorem
  • total variation distance

2010 MR Subject Classification

  • 15B52
  • 60B20
  • 60F10