Abstract
The first-passage time density, psi (r, t) (defined as the probability density for the time spent by a random walker to travel (for the first time) the distance r that separates the starting site from its nearest neighbours), and the survival probability S(r, t) (i.e. the probability that a random walker who starts at a site has not been absorbed by traps located on its nearest neighbours at distance r in the time interval (0, t)), were calculated for the class of deterministic fractals in which sites are isolated from the rest of the lattice by their nearest neighbours. The large xi identical to r/( square root (2Dt)1dw/) asymptotic expressions for these quantities are psi (r, t) approximately=A xi nu 2+dw/ exp(-C xi nu ) and h(r, t)=1-S(r, t) approximately=(A/C)(dw-1) xi - nu 2/exp(-C xi nu ) with v=dw/(dw-1), A and C being characteristic constants for each fractal. The asymptotic expression for S(r, t) is used to justify that, for this class of deterministic fractals, the propagator or Green function is given asymptotically by P(r, t)~t-ds/2 xi alpha exp(-C xi nu ) for large xi , with alpha = nu /2-df. This value of alpha differs from others proposed recently.