We calculate the exact autocorrelation exponent lambda and persistence
exponent theta, and also amplitudes, in the dilute limit of phase ord
ering for dimensions d greater than or equal to 2. In the Lifshitz-Sly
ozov-Wagner limit of conserved order parameter dynamics we iind theta
= gamma(d) epsilon, a universal constant times the volume fraction. Fo
r 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 t
he q --> infinity-state Ports model and soap froths, proposing new poi
soning exponents.