Repeated bond traversal probabilities for the simple random walk
Statistical Mechanics
2009-11-07 v1
Abstract
We consider the average number B_m(t) of bonds traversed exactly m times by a t step simple random walk. We determine B_m(t) explicitly in the scaling limit t -> oo with m/sqrt(t) fixed in dimension d=1 and m/log(t) fixed in dimension d=2. The scaling function is an erfc in d=1 and an exponential in d=2.
Keywords
Cite
@article{arxiv.cond-mat/0205594,
title = {Repeated bond traversal probabilities for the simple random walk},
author = {T. Antal and H. J. Hilhorst and R. K. P. Zia},
journal= {arXiv preprint arXiv:cond-mat/0205594},
year = {2009}
}
Comments
6 pages, 3 figures