  The probability distribution p(l) of an atom to return to a step at distance
l from the detachment site, with a random walk in between, is exactly
enumerated. In particular, we study the dependence of p(l) on step roughness,
presence of other reflecting or absorbing steps, interaction between steps and
diffusing atom, as well as concentration of defects on the terrace neighbouring
the step. Applying Monte Carlo techniques, the time evolution of equilibrium
step fluctuations is computed for specific forms of return probabilities.
Results are compared to previous theoretical and experimental findings.
