Limit theorems for 2D invasion percolation

M. Damron, A. Sapozhnikov

Research output: Book/ReportReportAcademic

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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 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.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages23
Publication statusPublished - 2010

Publication series

NameReport Eurandom
Volume2010040
ISSN (Print)1389-2355

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