Random walk on the infinite cluster of the percolation model
We consider random walk on the infinite cluster of bond percolation on \(\mathbb{Z}^ d\). We show that, in the supercritical regime when \(d \geq 3\), this random walk is a.s. transient. This conclusion is achieved by considering the infinite percolation cluster as a random electrical network in which each open edge has unit resistance. It is proved that the effective resistance of this network between a nominated point and the points at infinity is almost surely finite.
infinite percolation cluster as a random electrical network
scientific article; zbMATH DE number 569066