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May 2012 Limit theorems for 2D invasion percolation
Michael Damron, Artëm Sapozhnikov
Ann. Probab. 40(3): 893-920 (May 2012). DOI: 10.1214/10-AOP641

Abstract

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 nth of which gives the number of outlets in the box centered at the origin of side length 2n. 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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Michael Damron. Artëm Sapozhnikov. "Limit theorems for 2D invasion percolation." Ann. Probab. 40 (3) 893 - 920, May 2012. https://doi.org/10.1214/10-AOP641

Information

Published: May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1251.60071
MathSciNet: MR2962082
Digital Object Identifier: 10.1214/10-AOP641

Subjects:
Primary: 60K35 , 82B43

Keywords: central limit theorem , correlation length , Critical percolation , Invasion percolation , invasion ponds , near critical percolation , scaling relations

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 3 • May 2012
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