ON THE PROPAGATOR OF SIERPINSKI GASKETS

In this paper we present numerical calculations for the propagator P(r, t), the probability to reach a distance r at time t having started at the origin at t = 0, on Sierpinski gaskets. The results are confronted with approximate analytical expressions. It is shown that P(r, t) approximately t-d(s)/2-PI(xi), where xi is the scaling variable: xi = r/t1/d(w). In the short-xi regime the scaling function follows the form PI(xi) approximately exp(-c1-xi-d(w)), while for large xi, PI(xi) is given asymptotically by PI(xi) approximately xi-alpha exp(-c2-xi-nu), with alpha = (d(f) - d(w)/2)/(d(w) - 1) and nu = d(w)/(d(w) - 1). This result extends the previously derived expressions. The numerically observed oscillations which are superimposed on the power-law decay of the autocorrelation function P(r = 0, t) are analysed in terms of typical residence times on hierarchical substructures.