Microscopic densities and Fock-Sobolev spaces
Complex Variables
2019-10-07 v5 Mathematical Physics
math.MP
Abstract
We study two-dimensional eigenvalue ensembles close to certain types of singular points in the bulk of the droplet. We prove existence of a microscopic density which quickly approaches the classical equilibrium density, as the distance from the singularity increases beyond the microscopic scale. As a consequence we obtain asymptotics for the Bergman function of certain Fock-Sobolev spaces of entire functions.
Cite
@article{arxiv.1610.10052,
title = {Microscopic densities and Fock-Sobolev spaces},
author = {Yacin Ameur and Seong-Mi Seo},
journal= {arXiv preprint arXiv:1610.10052},
year = {2019}
}