Origin of power-law distributions in deterministic walks: the influence of landscape geometry.

Abstract

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular (ALxL) landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one (L-->0) and two (AL approximately L) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin striplike region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power-law distribution for the step lengths. The relevance of our findings in broader contexts--of both deterministic and random walks--is also briefly discussed.

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Cite this paper

@article{Santos2007OriginOP, title={Origin of power-law distributions in deterministic walks: the influence of landscape geometry.}, author={Marcos C Santos and Denis Boyer and Octavio Miramontes and G. M. Viswanathan and Ernesto P Raposo and Jos{\'e} L. Mateos and Marcos G E da Luz}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2007}, volume={75 6 Pt 1}, pages={061114} }