Limit theorems for beta-Jacobi ensembles | Zendy

Tiefeng Jiang | Zendy

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Limit theorems for beta-Jacobi ensembles

Author(s) -

Tiefeng Jiang

Publication year - 2013

Publication title -

bernoulli

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.814

H-Index - 72

eISSN - 1573-9759

pISSN - 1350-7265

DOI - 10.3150/12-bej495

Subject(s) - mathematics , eigenvalues and eigenvectors , limit (mathematics) , beta (programming language) , asymptotic distribution , central limit theorem , limiting , infinity , mathematical analysis , pure mathematics , statistics , quantum mechanics , mechanical engineering , physics , estimator , computer science , engineering , programming language

For a β-Jacobi ensemble determined by parameters a1 ,a 2 and n, under the restriction that the three parameters go to infinity with n and a1 being of small orders of a2, we obtain some limit theorems about the eigenvalues. In particular, we derive the asymptotic distributions for the largest and the smallest eigenvalues, the central limit theorems of the eigenvalues, and the limiting distributions of the empirical distributions of the eigenvalues.

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