Yacin Ameur

Two-dimensional Coulomb gas: fluctuations through a spectral gap

The talk will focus around some new results relating to fluctuations of smooth linear statistics of two-dimensional Coulomb gas ensembles, where the droplet is disconnected, i.e., it has some "spectral gaps". The particles which fall near the boundary of the gap come with an additional uncertainty, since there are several disjoint boundary components to choose from. For a class of radially symmetric model ensembles, we quantify this uncertainty in terms of the Jacobi theta function as well as a discrete Gaussian distribution. (Joint work with Christophe Charlier and Joakim Cronvall.)