  In this paper we present a study of the mixing time of a random walk on the
largest component of a supercritical random graph, also known as the giant
component. We identify local obstructions that slow down the random walk, when
the average degree d is at most (ln n lnln n)^{1/2}, proving that the mixing
time in this case is O((ln n/d)^2) asymptotically almost surely. As the average
degree grows these become negligible and it is the diameter of the largest
component that takes over, yielding mixing time O(ln n/ln d). We proved these
results during the 2003-04 academic year. Similar results but for constant d
were later proved independently by I. Benjamini, G. Kozma and N. Wormald.
