LOGARITHMIC CORRECTIONS IN THE SURVIVAL PROBABILITY FOR RANDOM-WALKS IN RANDOM TRAPPING ENVIRONMENTS

We study the survival probability of a particle that performs a random walk in a medium with traps where the trapping strength V is distributed randomly. We use an approach which is asymptotically exact and brings Wn(s), the number of distinct sites s visited after n steps, into play. Particularly in one dimension Wn(s) is known exactly and the survival probability for arbitrary potentials can be calculated. We find that for all distributions starting with a power law the survival probability is affected by universal logarithmic corrections, consistent with recent findings of Nieuwenhuizen and Luck. In the one-dimensional case we also give the prefactor and perform Monte Carlo simulations. We also study the survival probability for arbitrary dimensions and diffusion in lattice gases analytically for t→∞. © 1990.