Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters
成果类型：
Article
署名作者：
Damron, Michael; Sapozhnikov, Artem
署名单位：
Princeton University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-010-0274-y
发表日期：
2011
页码：
257-294
关键词：
摘要：
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 (IICs). 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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