Aging and its distribution in coarsening processes

We investigate the age distribution function P(tau,t) in prototypical coarsening processes. Here P(tau,t) is the probability density that in a time interval (0,r) a given site was last crossed by an interface in the coarsening process at time tau. We determine P(tau,t) exactly in one dimension for the (deterministic) two-velocity ballistic annihilation process and the !stochastic) infinite-state Potts model with zero-temperature Glauber dynamics. Surprisingly, we find that in the scaling limit, P(tau,t) is identical for these two models, We also show that the average age, i.e., the average time since a site was last visited by an interface, grows linearly with the observation time t. This latter property is also found in the one-dimensional Ising model with zero-temperature Glauber dynamics. We also discuss the age distribution in dimension d greater than or equal to 2 and find similar qualitative features to those in one dimension.