Repeated bond traversal probabilities for the simple random walk
T. Antal, H. J. Hilhorst, R. K. P. Zia
Abstract
We consider the average number Bm(t) of bonds traversed exactly m times by a t step simple random walk. We determine Bm(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.
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