Speaker
Dworaczek Guera, KTH Royal Institute of Technology
Abstract
In this joint work with Gaultier Lambert and Luke Peilen, we consider the intermediary temperature regime of β-ensembles \((i.e. 1/N<<β<<1)\) with real analytic potential. We exhibit a transition for the mesoscopic fluctuations in the bulk and show that there are two regimes: when the mesoscopic scale η is large enough, the fluctuations are like those for β constant and for small enough η, they are given by the underlying Poisson point process. The proof relies on the definition of a sequence of measures more precise than the equilibrium measure and two local laws in each regime.