Nonstandard Large and Moderate Deviations for the Laguerre Ensemble
Probability
2025-03-20 v1
Abstract
In this paper, we show limit theorems for the weighted spectral measure of the Laguerre ensemble under a nonstandard scaling, when the parameter grows faster than the matrix size. For this parameter scaling, the limit behavior is similar to the case of the Gaussian ensemble. We show a large deviation principle, moderate deviations and a CLT for the spectral measure. For the moderate deviations and the CLT, we observe a particular dependence on the rate of the parameter and a corrective shift by a signed measure. The proofs are based on the tridiagonal representation of the Laguerre ensemble.
Cite
@article{arxiv.2503.15347,
title = {Nonstandard Large and Moderate Deviations for the Laguerre Ensemble},
author = {Helene Götz and Jan Nagel},
journal= {arXiv preprint arXiv:2503.15347},
year = {2025}
}