On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble
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. CFL2021 and conduct an asymptotic analysis of the related exponential moments.
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