Limit theorems for Jacobi ensembles with large parameters

with parameters $k_{1}, k_{2}, k_{3} \geq 0$ . In the freezing case $(k_{1}, k_{2}, k_{3}) = κ \cdot (a, b, 1)$ with $a, b > 0$ fixed and $κ \to \infty$ , we derive a central limit theorem. The drift and covariance matrix of the limit are expressed via the zeros of classical Jacobi polynomials. We also determine the eigenvalues and eigenvectors of the covariance matrices. Our results are related to corresponding limits for $β$ -Hermite and Laguerre ensembles for $β \to \infty$ .

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Keywords

$\beta$-Jacobi ensembles, freezing, central limit theorems, zeros of Jacobi polynomials, eigenvalues of covariance matrices

Mathematical Subject Classification

Primary: 33C45, 60B20, 60F05, 70F10

Secondary: 33C67, 82C22

Milestones

Received: 23 November 2020

Revised: 18 December 2020

Accepted: 5 January 2021

Published: 20 October 2021

Authors

Kilian Hermann
Fakultät Mathematik Technische Universität Dortmund Germany

Michael Voit
Fakultät Mathematik Technische Universität Dortmund Germany

Vol. 3, No. 4, 2021

Kilian Hermann and Michael Voit

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors