Families of two-dimensional Coulomb gases on an ellipse: Correlation functions and universality

Abstract

We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature β = 2 we can use the technique of planar orthogonal polynomials, borrowed from random matrix theory, to explicitly determine all k-point correlation functions for a fixed number of particles N. These are given by the determinant of the kernel of the corresponding orthogonal polynomials, which in our case are the Gegenbauer polynomials, or a subset of the asymmetric Jacobi polynomials, depending on the choice of external potential, as shown in a companion paper recently published by..