Weighted Potential Theory & Partial Balayage

Sammanfattning: In random matrix theory it is known that the probability measure describing the spectral distribution of certain normal random matrices in the scaling limit tends to the equilibrium measure of an equilibrium problem in weighted potential theory. Motivated by this relation we compare the equilibrium measure of a sample Gaussian background potential perturbed by a point mass with a partial balayage operation of the point mass to a specific set, and get an indication of a general relation between the equilibrium problem of certain background potentials and a specific partial balayage operation. We develop this relation in detail and further discuss the possibility of an even more general method of obtaining the weighted equilibrium measure of a background potential directly through a certain partial balayage operation.