Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters

Abstract

We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IIC's). First we compute the exact decay rate of the distribution of both the weight of the kth outlet and the volume of the kth pond. Next we prove bounds for all moments of the distribution of the number of outlets in an annulus. This result leads to almost sure bounds for the number of outlets in a box B(2^n) and for the decay rate of the weight of the kth outlet to p_c. We then prove existence of multiple-armed IIC measures for any number of arms and for any color sequence which is alternating or monochromatic. We use these measures to study the invaded region near outlets and near edges in the invasion backbone far from the origin.

38 pages, 10 figures, added a thorough sketch of the proof of existence of IIC's with alternating or monochromatic arms (with some generalizations)

References in corpus (2)

• Relations between invasion percolation and critical percolation in two dimensions
• Lectures on two-dimensional critical percolation

Cited by in corpus (7)

• Scaling limit of the invasion percolation cluster on a regular tree
• Limit theorems for 2D invasion percolation
• Invasion percolation on the Poisson-weighted infinite tree
• Rotational invariance in critical planar lattice models
• Pivotal, cluster and interface measures for critical planar percolation
• Exponential growth of ponds in invasion percolation on regular trees
• The computation of generalized percolation critical polynomials by the deletion-contraction algorithm