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<p>We consider <i>β</i>-Jacobi ensembles with parameters <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub> ≥ <i>n</i>. We prove that the empirical measure of the rescaled <i>β</i>-Jacobi ensembles converges weakly to a modified Wachter law via the spectral measure method. We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.</p>

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Nonstandard Limit Theorems and Large Deviation for β-Jacobi Ensembles with a Different Scaling

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Yutao Ma,
  • Yonghua Mao,
  • Siyu Wang

摘要

We consider β-Jacobi ensembles with parameters p1, p2 ≥ n. We prove that the empirical measure of the rescaled β-Jacobi ensembles converges weakly to a modified Wachter law via the spectral measure method. We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.