Repeated bond traversal probabilities for the simple random walk
arXiv:cond-mat/0205594 · doi:10.1088/0305-4470/35/39/301
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.
6 pages, 3 figures