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 root = - ln/In(t) [with lambda = - ln(l - c)], in two dimensions, and for -t(-1/3) ln[P(c, t)] vs t(2/3) lambda in three dimensions. These predictions are well supported by the Monte Carlo results.