高温区域高斯β系综的大偏差原理
A large deviation principle for the Gaussian beta ensemble in the high temperature regime
AI总结：
本文证明了高温区域高斯β系综加权谱测度的大偏差原理，其速率函数仅对离散测度有限，且在极高温时额外惩罚多余支撑点。
AI中文摘要：
我们证明了在高温区域，当$n\beta_n\to 2c \in [0,\infty)$时，高斯β系综的加权谱测度满足大偏差原理。所得速率函数具有新颖且有趣的结构：它仅对离散测度有限，并且，在极高温区域（当$c=0$时），可能会出现额外的项，这些项会惩罚第一个支撑点之外的每个支撑点。
英文摘要：
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.
