Helene Götz | Search arXiv

arXiv2026

A large deviation principle for the Gaussian beta ensemble in the high temperature regime

We show a large deviation principle for the weighted spectral measure of the Gaussian beta ensemble in the high temperature regime, when $nβ_n\to 2c \in [0,\infty)$. The resulting rate function has a novel and interesting structure: it is finite only for discrete measures and moreover, in the very high-temperature regime (when $c=0$), additional terms may arise that penalize each support point beyond the first.

math.PR↗

arXiv2026

Nonstandard Large and Moderate Deviations for the Laguerre Ensemble

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.

math.PR↗