Asymptotic form for random walk survival probabilities on three-dimensional lattices with traps

The problem of calculating statistics of time-to-trapping of a random walker on a trap-filled lattice is of interest in solid state physics. Several authors have suggested approximate methods for calculating the average survival probabilities. Here, an exact asymptotic form for the probability that an n step random walk visits S(n) distinct sites is used to ascertain the validity of a simple approximation suggested by Rosenstock. For trap concentrations below 0.05, the relative error in using Rosenstock's approximation is less than 10%.