A Central Limit Theorem for Fluctuations in Polyanalytic Ginibre Ensembles
Abstract
We study fluctuations of linear statistics in Polyanalytic Ginibre ensembles, a family of point processes describing planar free fermions in a uniform magnetic field at higher Landau levels. Our main result is asymptotic normality of fluctuations, extending a result of Rider and Vir\'ag. As in the analytic case, the variance is composed of independent terms from the bulk and the boundary. Our methods rely on a structural formula for polyanalytic polynomial Bergman kernels which separates out the different pure -analytic kernels corresponding to different Landau levels. The fluctuations with respect to these pure -analytic Ginibre ensembles are also studied, and a central limit theorem is proved. The results suggest a stabilizing effect on the variance when the different Landau levels are combined together.
Cite
@article{arxiv.1612.07974,
title = {A Central Limit Theorem for Fluctuations in Polyanalytic Ginibre Ensembles},
author = {Antti Haimi and Aron Wennman},
journal= {arXiv preprint arXiv:1612.07974},
year = {2016}
}