Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Götz, Helene, Nagel, Jan
Institution: TU Dortmund University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7214011745