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Non-extensive random walks

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  • Anteneodo, C.

Abstract

Stochastic variables whose addition leads to q-Gaussian distributions Gq(x)∝[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.

Suggested Citation

  • Anteneodo, C., 2005. "Non-extensive random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(2), pages 289-298.
    • Handle: RePEc:eee:phsmap:v:358:y:2005:i:2:p:289-298
    DOI: 10.1016/j.physa.2005.06.052
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    Cited by:

    1. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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