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Repeated bond traversal probabilities for the simple random walk

T. Antal·H. J. Hilhorst·R. K. P. Zia
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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.

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T. Antal, H. J. Hilhorst, R. K. P. Zia. 2002-05-28. Repeated bond traversal probabilities for the simple random walk. https://doi.org/10.1088/0305-4470%2F35%2F39%2F301

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