Diffusion with Random Distribution of Static Traps

The survival probability P(c,t) of a random walk of t steps with static traps at concentration c is studied in two and three dimensions by an efficient Monte Carlo method based on a mapping onto a polymer model. On the basis of the theoretical work of Donsker and Varadhan [Commun. Pure Appl. Math. 28, 525 (1975); 32, 721 (1979)] and of Rosenstock [J. Math. Phys. (N.Y.) 11, 487 (1970)] one expects a data collapse for -ln[P(c,t)]/ln(t) plotted vs √λt/ln(t) [with λ = -ln(1-c)], in two dimensions, and for -t^-1/3ln[P(c,t)] vs t^2/3λ in three dimensions. These predictions are well supported by the Monte Carlo results.