Large deviations of crowding in finite $\beta$-ensembles

Kartick Adhikari, Sitanath Majumder

We consider finite $\beta$-ensembles ${\mathcal{X}}_{n,\beta }^{\mathbb{F}}$ with $n$ points on $\mathbb{F}$, where $\mathbb{F}$ denotes either the real line or the complex plane. Let $U$ be a bo…