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

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

2009-03-26

arxiv.org/abs/0903.4496v2

Probab. Theory Relat. Fields, Vol. 150 (2011), 257-294

Mathematics

Probability

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

Scientific paper

10.1007/s00440-010-0274-y

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.

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