Abstract
Under the assumption of slow evolution of the cluster structure of walker positions, the kinetic equation is derived, according to which the Lévy law is fulfilled on the mesoscopic time-scale, while the system tends to the generalized Tsallis distribution on the macroscopic time-scale. The asymptotics are found for the time dependences of the hierarchy characteristic scale and the probability distribution over the hierarchical levels.
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Translated from Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 71, No. 7, 2000, pp. 412–417.
Original Russian Text Copyright © 2000 by Olemsko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \).