Random walk hitting times and effective resistance in sparsely connected Erdos-Renyi random graphs

We prove a bound on the effective resistance R ( x , y ) between two vertices x , y of a connected graph which contains a suitably well-connected subgraph. We apply this bound to the Erdos-Renyi random graph G ( n , p ) with n p = omega ( log n ), proving that R ( x , y ) concentrates around 1 / d ( x ) + 1 / d ( y ), that is, the sum of reciprocal degrees. We also prove expectation and concentration results for the random walk hitting times, Kirchoff index, cover cost, and the random target time (Kemeny's constant) on G ( n , p ) in the sparsely connected regime log n + log log log n <= n p < n 1 / 10.