Long Time Tail for Random Walk in Random Scenery

摘要

A simple random walk on a lattice whose sites are colored black or white independently with probabilities q and 1-q is considered. Walk and coloring are independent. The asymptotic behavior of the interarrival times between successive visits of the walk to the black sites is determined. In particular, a long time tail occurs in the decay of the average interarrival times to a limiting value.