On the emergence of asymptotic localization for some random diffusion processes

Interpreting intermittency as the result of a cascade through a random medium, it is shown that the long time behaviour of the D-dimensional random heat equation generates intermittent patterns as well as a multifractal structure. Intermittent fluctuations are arranged in a hierarchical fashion. Moreover, multifractal analysis reveals that the cascading system organizes itself into a point-like set of «spikes» whose statistical properties are given. Such «spikes» are similar to localized asymptotic states. This allows one to sketch out possible applications to «non-thermal» transitions in multiparticle production