Two-dimensional random walk in a bounded domain
Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics - 1/AF Bidhan Nagar, Kolkata, 700064 India
Corresponding author: firstname.lastname@example.org
Accepted: 3 June 2010
In a recent letter Ciftci and Cakmak (EPL, 87 (2009) 60003) showed that the two-dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near the 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 curve which bounds this distribution.
PACS: 05.40.Fb – Random walks and Levy flights / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2010