  We study the asymptotic behavior the exit times of random walk from Euclidean
balls around the origin of the incipient infinite cluster in a manner inspired
by [26]. We do this by obtaining bounds on the effective resistance between the
origin and the boundary of these Euclidean balls. We show that the geometric
properties of long-range percolation clusters are significantly different from
those of finite-range clusters. We also study the behavior of random walk on
the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds
for the incipient infinite cluster in high dimensions, both for long-range
percolation and for finite-range percolation.
