Large deviations of empirical measures under symmetric interaction (Q1426858)

The author proves the large deviation principle for the joint empirical measure of pairs of random variables which are coupled by a ``totally symmetric'' interaction. The rate function is given by an explicit bilinear expression, which is finite only on product measures and hence is non-convex. As a corollary, he derives a large deviations principle for the univariate average empirical measures with a rate function that superficially resembles the rate function of random matrices.