MULTILEVEL LARGE DEVIATIONS AND INTERACTING DIFFUSIONS

Let (xi(N)) be a sequence of random variables with values in a topolog ical space which satisfy the large deviation principle. For each M and each N, let XI(M, N) denote the empirical measure associated with M i ndependent copies of xi(N). As a main result, we show that (XI(M, N)) also satisfies the large deviation principle as M, N --> infinity . We derive several representations of the associated rate function. These results are then applied to empirical measure processes XI(M, N)(t) = M-1SIGMA(i = 1) M delta(xiiN(t), 0 less-than-or-equal-to t less-than- or-equal-to T, where (xi1N(t),..., xi(M)N(t)) is a system of weakly in teracting diffusions with noise intensity 1/N. This is a continuation of our previous work on the McKean-Vlasov limit and related hierarchic al models ([4], [5]).