Non-anomalous diffusion is not always Gaussian

Regular Article

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.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Giuseppe Forte
    • 1
  • Fabio Cecconi
    • 2
  • Angelo Vulpiani
    • 1
    • 2
  1. 1.Dipartimento di FisicaUniversità di Roma “Sapienza”RomaItaly
  2. 2.CNR-Istituto dei Sistemi Complessi (ISC)UOS “Sapienza”RomaItaly

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