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arXiv · 0910.5885

Two-dimensional random walk in a bounded domain

Mahashweta Basu·P. K. Mohanty
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Abstract

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.

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Mahashweta Basu, P. K. Mohanty. 2010-03-09. Two-dimensional random walk in a bounded domain. https://doi.org/10.1209/0295-5075%2F90%2F50005

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