A central limit theorem for the average target hitting time for a random walk on a random graph

Consider simple random walk on a realization of an Erdős-Renyi 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 πᵢ, the invariant measure of the random walk.