Nonstandard Large and Moderate Deviations for the Laguerre Ensemble

Helene Götz; Jan Nagel

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arXiv · 2503.15347

Nonstandard Large and Moderate Deviations for the Laguerre Ensemble

Helene Götz·Jan Nagel

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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.

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BibTeX RIS

Helene Götz, Jan Nagel. 2025-03-19. Nonstandard Large and Moderate Deviations for the Laguerre Ensemble. https://arxiv.org/abs/2503.15347

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