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Issue 31, 2018
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Fluctuations of random walks in critical random environments

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Abstract

Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.

Graphical abstract: Fluctuations of random walks in critical random environments

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Publication details

The article was received on 20 May 2018, accepted on 19 Jul 2018 and first published on 19 Jul 2018


Article type: Paper
DOI: 10.1039/C8CP03212B
Citation: Phys. Chem. Chem. Phys., 2018,20, 20427-20438
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    Fluctuations of random walks in critical random environments

    Y. Mardoukhi, J. Jeon, A. V. Chechkin and R. Metzler, Phys. Chem. Chem. Phys., 2018, 20, 20427
    DOI: 10.1039/C8CP03212B

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