Repeated bond traversal probabilities for the simple random walk
  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. 
T. Antal, H.J. Hilhorst, and R.K.P. Zia