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Non-anomalous diffusion is not always Gaussian

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Abstract

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ⟨x(t)q⟩ for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “Sapienza”, P.le A. Moro 2, 00185, Roma, Italy

    Giuseppe Forte & Angelo Vulpiani

  2. CNR-Istituto dei Sistemi Complessi (ISC), UOS “Sapienza”, P.le A. Moro 2, 00185, Roma, Italy

    Fabio Cecconi & Angelo Vulpiani

Authors
  1. Giuseppe Forte
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  2. Fabio Cecconi
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  3. Angelo Vulpiani
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Correspondence to Fabio Cecconi.

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Forte, G., Cecconi, F. & Vulpiani, A. Non-anomalous diffusion is not always Gaussian. Eur. Phys. J. B 87, 102 (2014). https://doi.org/10.1140/epjb/e2014-40956-0

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  • DOI: https://doi.org/10.1140/epjb/e2014-40956-0

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