Large deviations for empirical measures with degenerate limiting distribution (Q1326247)

This paper studies the large deviations of the empirical measure associated with \(n\) independent random variables with a degenerate limiting distribution as \(n\to\infty\). A large deviations principle -- quite unlike the classical Sanov type results -- is established for such empirical measures in a general Polish space setting. This result is applied to the large deviations for the empirical process of a system of interacting particles, in which the diffusion coefficient vanishes as the number of particles tends to infinity. A second way in which the present example differs from previous work on similar weakly interacting systems is that there is a singularity in the mean-field type interaction.