Large deviations for empirical measures with degenerate limiting distribution

Summary

This paper studies the large deviations of the empirical measure associated withn independent random variables with a degenerate limiting distribution asn→∞. 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.