Persistence, poisoning, and autocorrelations in dilute coarsening

We calculate the exact autocorrelation exponent lambda and persistence exponent theta, and also amplitudes, in the dilute limit of phase ordering for dimensions d greater than or equal to 2. In the Lifshitz-Slyozov-Wagner limit of conserved order parameter dynamics we iind theta = gamma(d) epsilon, a universal constant times the volume fraction. For autocorrelations, lambda = d at intermediate times, with a late time crossover to lambda greater than or equal to d/2 + 2. We also derive lambda and theta for globally conserved dynamics and relate these to the q --> infinity-state Ports model and soap froths, proposing new poisoning exponents.