Concentration of hitting times in Erdős‐Rényi graphs

Abstract

AbstractWe consider Erdős‐Rényi graphs for fixed and and study the expected number of steps, , that a random walk started in needs to first arrive in . A natural guess is that an Erdős‐Rényi random graph is so homogeneous that it does not really distinguish between vertices and . Löwe‐Terveer established a CLT for the Mean Starting Hitting Time suggesting . We prove the existence of a strong concentration phenomenon: is given, up to a very small error of size , by an explicit simple formula involving only the total number of edges , the degree and the distance .