Local time of random walks on graphs

TL;DR

This paper develops a general method to compute the local time of random walks on graphs using the resolvent of the transition matrix, aiding in understanding occupation times in network structures.

Contribution

Introduces a novel approach to calculate local time functionals of random walks on graphs via the resolvent of the transition matrix.

Findings

Method for calculating sample-path averages of local time functionals.

Applicable to generic graphs for analyzing occupation times.

Provides a theoretical framework for future studies on random walks.

Abstract

We investigate the local (or occupation) time of a discrete-time random walk on a generic graph, and present a general method for calculating sample-path averages of local time functionals in terms of the resolvent of the transition matrix.