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arXiv · 2607.11547

On The Eigenvalue Rigidity of the Laguerre Unitary Ensemble

Chenhao Lu·Xiaolu Yue
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Abstract

In this paper, we establish an optimal global rigidity estimate for the eigenvalues of the Laguerre unitary ensemble. Using the central limit theorem, we first construct a random measure via the eigenvalue counting function and then prove its convergence to a Gaussian multiplicative chaos measure, which yields the desired rigidity result. To prove this convergence, we apply a sufficient condition due to Claeys et al.[7] and carry out an asymptotic analysis of the corresponding exponential moments.

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Chenhao Lu, Xiaolu Yue. 2026-07-13. On The Eigenvalue Rigidity of the Laguerre Unitary Ensemble. https://arxiv.org/abs/2607.11547

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