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We investigate a two-dimensional statistical model of N charged particlesinteracting via logarithmic repulsion in the presence of an oppositely chargedcompact region K whose charge density is determined by its equilibriumpotential at an inverse temperature corresponding to \beta = 2. When the chargeon the region, s, is greater than N, the particles accumulate in a neighborhoodof the boundary of K, and form a determinantal point process on the complexplane. We investigate the scaling limit, as N \to \infty, of the associatedkernel in the neighborhood of a point on the boundary under the assumption thatthe boundary is sufficiently smooth. We find that the limiting kernel dependson the limiting value of N/s, and prove universality for these kernels. Thatis, we show that, the scaled kernel in a neighborhood of a point \zeta \in\partial K can be succinctly expressed in terms of the scaled kernel for theclosed unit disk, and the exterior conformal map which carries the complement Kto the complement of the closed unit disk. When N / s \to 0 we recover theuniversal kernel discovered by Doron Lubinsky in Universality type limits forBergman orthogonal polynomials, Comput. Methods Funct. Theory, 10:135-154,2010.

Universality for ensembles of matrices with potential theoretic weights on domains with smooth boundary