Speaker
Sylvia Serfaty, NYU Courant
Abstract
We are interested in Riesz gases which are ensembles of points with pair interaction of the form |x|^{-s}, with a confining potential, in the range s\in [d-2,d), where d is the dimension. This includes the Coulomb case s=d-2 and the logarithmic cases s=0 in dimensions 1 and 2. While fluctuations of log gases in dimensions 1 and 2 are now well understood, with results of CLT type and convergence to the GFF, we turn to the general Riesz case which presents new challenges. We report on work in progress with Luke Peilen that establishes a CLT for s>0 small enough.