On large deviations for the empirical measures of weakly interacting systems

Markus Fischer (University of Padua)
Wednesday, July 11, 2012 - 5:00pm
TU Berlin, MA041, Strasse des 17. Juni 136, 10623 Berlin

One of the basic results of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies a large deviation principle with rate function given by relative entropy with respect to the common sample distribution. Large deviation principles for the empirical measures are known to hold also for broad classes of weakly interacting systems (or mean field systems). In cases in which the interaction through the empirical measure corresponds to an absolutely continuous change of measure, the large deviations rate function can be expressed as relative entropy of a distribution with respect to the law of the McKean-Vlasov limit with measure-variable frozen at that distribution. This form of the rate function is a natural generalization of Sanov’s theorem. We discuss situations (beyond that of tilted distributions) in which a large deviation principle holds with rate function in relative entropy form.