Invasion percolation on regular trees

Invasion percolation is a dynamic
process closely linked to critical percolation,
but without an external parameter. In joint
work with Omer Angel, Frank den Hollander and
Gord Slade we showed that the cluster of invaded
points consists of a backbone together with
sub-critical trees hanging off the backbone, with
parameters that increase towards criticality. By
this analysis we derive scaling estimates for the
r-point functions and related quantities, and show
that the scaling behaviour differs from the incipient
infinite cluster. In ongoing joint work with
Mathieu Merle, we also analyze the continuum limit
of the random trees obtained in invasion percolation.