Two-dimensional random walk in a bounded domain
Statistical Mechanics
2010-09-03 v2 General Physics
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.
Cite
@article{arxiv.0910.5885,
title = {Two-dimensional random walk in a bounded domain},
author = {Mahashweta Basu and P. K. Mohanty},
journal= {arXiv preprint arXiv:0910.5885},
year = {2010}
}
Comments
4 pages, 7 eps figures, revtex4