Non-extensive random walks

Stochastic variables whose addition leads to q-Gaussian distributions G(q)(chi) proportional to [1 + (q - 1) beta chi(2)](+)(1/(1-q)) (with beta > 0, 1 <= q < 3 and where [f(chi)](+) = max{f (chi), 0}) as limit law for a large number of terms are investigated. Randoin walk sequences related to this problem possess a simple additive-multiplicative structure commonly found in several contexts, thus justifying the ubiquity of those distributions. A characterization of the statistical properties of the random walk step lengths is performed. Moreover, a connection with lion-linear stochastic processes is exhibited. q-Gaussian distributions have special relevance within the framework of non-extensive statistical mechanics, a generalization of the standard Boltzmann-Gibbs formalism, introduced by Tsallis over one decade ago. Therefore, the present findings may give insights on the domain of applicability of such generalization. (c) 2005 Elsevier B.V. All rights reserved.