Large deviations for empirical measures with degenerate limiting distribution

This paper studies the large deviations of the empirical measure associated with n independent random variables with a degenerate limiting distribution as n?8. 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. © 1993 Springer-Verlag.