The Annals of Probability

Limit theorems for 2D invasion percolation

Michael Damron and Artëm Sapozhnikov

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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.

Article information

Source
Ann. Probab., Volume 40, Number 3 (2012), 893-920.

Dates
First available in Project Euclid: 4 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.aop/1336136054

Digital Object Identifier
doi:10.1214/10-AOP641

Mathematical Reviews number (MathSciNet)
MR2962082

Zentralblatt MATH identifier
1251.60071

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35]

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

Citation

Damron, Michael; Sapozhnikov, Artëm. Limit theorems for 2D invasion percolation. Ann. Probab. 40 (2012), no. 3, 893--920. doi:10.1214/10-AOP641. https://projecteuclid.org/euclid.aop/1336136054


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