Eur. Phys. J. B (2014) 87: 102
https://doi.org/10.1140/epjb/e2014-40956-0

Regular Article

Non-anomalous diffusion is not always Gaussian

¹ Dipartimento di Fisica Università di Roma “Sapienza”, P.le A. Moro 2, 00185 Roma, Italy
² CNR-Istituto dei Sistemi Complessi (ISC), UOS “Sapienza”, P.le A. Moro 2, 00185 Roma, Italy

^a e-mail: fabio.cecconi@roma1.infn.it

Received: 25 October 2013
Received in final form: 20 March 2014
Published online: 1 May 2014

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.