First exit times and residence times for discrete random walks on finite lattices

TL;DR

This paper derives explicit formulas for key quantities like first exit times and residence times of discrete random walks on finite lattices, applicable to various potential landscapes and dynamic processes.

Contribution

It introduces new explicit formulas for surface-averaged first exit times and residence times, including complex scenarios like multiple particles and reflecting surfaces.

Findings

Explicit formulas for first exit times derived

Residence times for subvolumes computed

Analysis includes multiple particles and surface hits

Abstract

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 non-trivial potential landscape. We also compute quantities of interest for modelling 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.