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Nonstandard limit theorems and large deviation for beta -Jacobi ensembles with a different scaling
Yutao Ma, Yong-Hua Mao, Siyu Wang · 2023-07-28 · via math.PR updates on arXiv.org

We consider $β$-Jacobi ensembles with parameters $p_1, p_2\geq n.$ We prove that the empirical measure of the rescaled Jacobi ensembles converges weakly to a modified Watcher law via the spectral measure method, which revisits the weak limits obtained in \cite{MaLDPJ} while replacing the condition $βn\!>\!> \log n$ by $βn\!>\!>1.$ We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.

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