Some recent variations on the expected number of distinct sites visited by an n-step random walk

Asymptotic forms for the expected number of distinct sites visited by an n-step random walk, being calculable for many random walks, have been used in a number of analyses of physical models. We describe three recent extensions of the problem, the first replacing the single random walker by N→∞ random walkers, the second to the study of a random walk in the presence of a trapping site, and the third to a random walk in the presence of a trapping hyperplane.