Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9727507 | Physica A: Statistical Mechanics and its Applications | 2005 | 10 Pages |
Abstract
Stochastic variables whose addition leads to q-Gaussian distributions Gq(x)â[1+(q-1)βx2]+1/(1-q) (with β>0, 1⩽q<3 and where [f(x)]+=max{f(x),0}) as limit law for a large number of terms are investigated. Random 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 non-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.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
C. Anteneodo,