Beta Jacobi Ensembles and Associated Jacobi Polynomials

Hoang Dung Trinh, Khanh Duy Trinh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper deals with beta Jacobi ensembles, the type with the Jacobi weight. Making use of the random matrix model, we show that in the regime where βN→ const∈ [0 , ∞) , with N the system size, the empirical distribution of the eigenvalues converges weakly to a limiting measure which belongs to a new class of probability measures of associated Jacobi polynomials. This is analogous to the existing results for the other two classical weights. We also study the limiting behavior of the empirical measure process of beta Jacobi processes in the same regime and obtain a dynamical version of the above.

Original languageEnglish
Article number4
JournalJournal of Statistical Physics
Issue number1
Publication statusPublished - 2021 Oct


  • Associated Jacobi polynomials
  • Beta Jacobi ensembles
  • Beta Jacobi processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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