Invasion Percolation on the Cayley Tree: Exact Solution of a Modified Percolation Model

Abstract

A modified form of percolation theory is solved exactly on a Cayley tree of arbitrary coordination number. In this model, cluster growth proceeds "dynamically" by invasion along a path of least resistance. Although there are clear parallels to ordinary "static" percolation at the percolation threshold, there are also significant differences. In particular, the scaling function which describes the shape of large clusters is different in the two models.