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Random walks exhibiting anomalous diffusion: Elephants, urns and the limits of normality

Kearney, Michael and Martin, Richard J (2018) Random walks exhibiting anomalous diffusion: Elephants, urns and the limits of normality Journal of Statistical Mechanics: Theory and Experiment, 013209.

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A random walk model is presented which exhibits a transition from standard to anomalous diffusion as a parameter is varied. The model is a variant on the elephant random walk and differs in respect of the treatment of the initial state, which in the present work consists of a given number N of fixed steps. This also links the elephant random walk to other types of history dependent random walk. As well as being amenable to direct analysis, the model is shown to be asymptotically equivalent to a non-linear urn process. This provides fresh insights into the limiting form of the distribution of the walker’s position at large times. Although the distribution is intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to normal form when N is large under quite general conditions.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Martin, Richard J
Date : 22 January 2018
DOI : 10.1088/1742-5468/aaa38a
Copyright Disclaimer : © 2018 IOP Publishing Ltd and SISSA Medialab srl
Uncontrolled Keywords : Diffusion; Stochastic particle dynamics; Stochastic processes
Depositing User : Clive Harris
Date Deposited : 08 Jan 2018 14:29
Last Modified : 23 Jan 2019 02:08

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