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arXiv · 0705.4438

The origin of power-law distributions in deterministic walks: the influence of landscape geometry

M. C. Santos·D. Boyer·O. Miramontes·G. M. Viswanathan·E. P. Raposo·J. L. Mateos·M. G. E. da Luz
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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 ($A/L \times L)$ landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one ($L \to 0$) and two ($A/L \sim L$) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin strip-like 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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M. C. Santos, D. Boyer, O. Miramontes, G. M. Viswanathan, E. P. Raposo, J. L. Mateos, M. G. E. da Luz. 2007-05-30. The origin of power-law distributions in deterministic walks: the influence of landscape geometry. https://doi.org/10.1103/physreve.75.061114

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