A Central Limit Theorem for the average target hitting time for a random walk on a random graph

Matthias Löwe, Sara Terveer

Published 2021-04-02Version 1

Consider simple random walk on a realization of an Erd\H{o}s-R\'enyi graph. Assume that it is asymptotically almost surely (a.a.s.) connected. We prove a Central Limit Theorem (CLT) for the average target hitting time. By the latter we mean the expected time it takes the random walk on average to first hit a vertex $j$ when starting in a fixed vertex $i$. The average is taken with respect to $\pi_i$, the invariant measure of the random walk.