# Random walks on percolation clusters

## Speaker:

## Institution:

## Time:

## Location:

This talk will discuss random walks on percolation clusters.

The first case is supercritical ($p>p_c$) bond percolation in

$Z^d$. Here one can obtain Aronsen type bounds on the transition

probabilities, using analytic methods based on ideas of Nash.

For the critical case ($p=p_c$) one needs to study the incipient

infinite cluster (IIC). The easiest situation is the IIC on trees -

where the methods described above lead to an alternative approach to

results of Kesten (1986). (This case is joint work with T. Kumagai).