On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble

Dan Dai; Chenhao Lu

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arXiv · 2511.18967

On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble

Dan Dai·Chenhao Lu

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Abstract

In this paper, we prove an optimal global rigidity estimate for the eigenvalues of the Jacobi unitary ensemble. Our approach begins by constructing a random measure defined through the eigenvalue counting function. We then prove its convergence to a Gaussian multiplicative chaos measure, which leads to the desired rigidity result. To establish this convergence, we apply a sufficient condition from Claeys et al. \cite{CFL2021} and conduct an asymptotic analysis of the related exponential moments.

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Dan Dai, Chenhao Lu. 2025-11-24. On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble. https://arxiv.org/abs/2511.18967

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