Hitting and commute time distributions of restarting random walks on path graphs

Abstract

We calculate the probability mass function (PMF) and cumulative distribution function (CDF) of hitting and commute time for random walks with restarting on path graphs according to the exact expressions obtained by Zlatanov and Kocarev. The inclusion of a restarting mechanism on the path graph significantly reduces the probability that the walker completes a hit or commute, as shown by both the PMF and CDF. This means that it is less likely for a walker on a path graph to hit a given target node, or to commute from a target node back to the initial node.