Limit theorems for 2D invasion percolation

Details Limit theorems for 2D invasion percolation Limit theorems for 2D invasion percolation

2010-05-31

arxiv.org/abs/1005.5696v2

Mathematics

Probability

23 pages, 2 figures. Added details for most of the proofs and corrected the statement of Corollary 7. Added an appendix relate

Scientific paper

We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence (O(n)) of outlet variables, the n-th of which gives the number of outlets in the box centered at the origin of side length 2^n. The most important of these properties describes the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for (O(n)). We then show consequences of these limit theorems for the pond radii and outlet weights.

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