Hitting times in the binomial random graph

Fix k≥ 2, choose log nn(k-1)/k≤ p≤ 1-Ω(log⁴ n/n), and consider G~ G(n,p). For any pair of vertices v,w∈ V(G), we give a simple and precise formula for the expected number of steps that a random walk on G starting at w needs to first arrive at v. The formula only depends on basic structural properties of G. This improves and extends recent results of Ottolini and Steinerberger, as well as Ottolini, who considered this problem for constant as well as for mildly vanishing p.