Section: New Results

CLT for Circular beta-Ensembles at High Temperature

In [33], A. Hardy and G. Lambert have obtained a central limit theorem for the 2D Coulomb gas particle system constrained on a circle in the high temperature regime. An interesting feature is that the limiting variance interpolates between the Lebesgue $L^2$ norm, corresponding to the infinite temperature setting, and the Sobolev $H^{1/2}$ seminorm, corresponding to the zero temperature regime.