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The random walk problem is studied in two and three dimensions in thepresence of a random distribution of static traps. An efficient Monte Carlomethod, based on a mapping onto a polymer model, is used to measure thesurvival probability P(c,t) as a function of the trap concentration c and thetime t. Theoretical arguments are presented, based on earlier work of Donskerand Varadhan and of Rosenstock, why in two dimensions one expects a datacollapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambdat)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expectsa data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function oft^{2/3}lambda. These arguments are supported by the Monte Carlo results. Bothdata collapses show a clear crossover from the early-time Rosenstock behaviorto Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

Diffusion with Random Distribution of Static Traps