Hitting and trapping times on branched structures

Abstract

In this work we consider a simple random walk embedded in a generic branched structure and we find a close-form formula to calculate the hitting time Hi,f between two arbitrary nodes i and j. We then use this formula to obtain the set of hitting times Hi,f for combs and their expectation values, namely, the mean first-passage time, where the average is performed over the initial node while the final node f is given, and the global mean first-passage time, where the average is performed over both the initial and the final node. Finally, we discuss applications in the context of reaction-diffusion problems.