Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets (Q365721)

An ensemble of \(N\) charged particles in the 2D-electrostatical model is considered. The appearance of the system at a given state \(\{z_1,\dots,z_N\}\) is characterized by the probability density and the empirical measure \(\omega\) associated to the above state. The author examines two questions: (first) what is the probability to find the system (empirical measure \(\omega\)) close to a given Borel measure on the complex plane; (second) what is the limiting behaviour of the marginal probabilities of the probability density function for this system. New limit formulas are obtained to answer the above questions.