Many dispersive processes have moments of displacements with large-t behavior〈∣ x∣
p〉∼ tγp. The study of γp as a function of p provides a more complete characterization of the
process than does the single number γ2. Also at long times, the core of the concentration
relaxes to a self-similar profile, while the large-x tails, consisting of particles which have
experienced exceptional displacements, are not self-similar. Depending on the particular
process, the effect of the tails can be negligible and then γp is a linear function of p (strong …