2025/11/24 by Dai, Dan, Lu, Chenhao
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.2511.18967
openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28
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. \citeCFL2021 and conduct an asymptotic analysis of the related exponential moments.