Non-monotonic displacement distribution of active random walkers

We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions the distribution is non-monotonic and we show analytically...

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Bibliographic Details
Published inarXiv.org
Main Authors Teomy, Eial, Roichman, Yael, Shokef, Yair
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.08.2019
Subjects
Active control
Distribution functions
Economic models
Motion control
Physics - Statistical Mechanics
Probability distribution functions
Random walk
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Summary:We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions the distribution is non-monotonic and we show analytically and numerically that the existence of the non-monotonicity is governed by the walker's tendency to move forward, while the correlations between the timing of its active motion control the magnitude and shape of the non-monotonicity. In particular, we find that in a homogeneous system such non-monotonicity can occur only if the persistence is strong enough.
ISSN:2331-8422
DOI:10.48550/arxiv.1908.07242