Beta Jacobi Ensembles and Associated Jacobi Polynomials

Hoang Dung Trinh, Khanh Duy Trinh*

*この研究の対応する著者

研究成果査読

抄録

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.

本文言語English
論文番号4
ジャーナルJournal of Statistical Physics
185
1
DOI
出版ステータスPublished - 2021 10

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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