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

Source 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.