Large Deviations and Linear Statistics for Potential Theoretic Ensembles Associated with Regular Closed Sets

A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse temperature \beta is investigated. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a point process in the complex plane. We describe the weak* limits of the joint intensities of this point process and show that it is exponentially likely to find the process in a neighborhood of the equilibrium measure for K.