Two-Dimensional Coulomb Gas on an Elliptic Annulus

Abstract: It is well-known that two-dimensional Coulomb gases at a special inverse temperature $\beta = 2$ can be analyzed by using the orthogonal polynomial method borrowed from the theory of random matrices. In this paper, such Coulomb gas molecules are studied when they are distributed on an elliptic annulus, and the asymptotic forms of the molecule correlation functions in the thermodynamic limit are evaluated. For that purpose, two-dimensional orthogonality relations of the Chebyshev polynomials on an elliptic annulus are utilized.