First-exit times and residence times for discrete random walks on finite lattices -: art. no. 016127

In this paper, we derive explicit formulas for the surface averaged first-exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a nontrivial potential landscape. We also compute quantities of interest for modeling surface reactions and other dynamic processes, such as the residence time in a subvolume, the joint residence time of several particles, and the number of hits on a reflecting surface.