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• W2107449886 abstract "We study invasion percolation in two dimensions. We compare connectivity properties of the origin’s invaded region to those of (a) the critical percolation cluster of the origin and (b) the incipient infinite cluster. To exhibit similarities, we show that for any k≥1, the k-point function of the first so-called pond has the same asymptotic behavior as the probability that k points are in the critical cluster of the origin. More prominent, though, are the differences. We show that there are infinitely many ponds that contain many large disjoint pc-open clusters. Further, for k>1, we compute the exact decay rate of the distribution of the radius of the kth pond and see that it differs from that of the radius of the critical cluster of the origin. We finish by showing that the invasion percolation measure and the incipient infinite cluster measure are mutually singular." @default.
• W2107449886 created "2016-06-24" @default.
• W2107449886 creator A5020667922 @default.
• W2107449886 creator A5050608628 @default.
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• W2107449886 date "2009-11-01" @default.
• W2107449886 modified "2023-09-27" @default.
• W2107449886 title "Relations between invasion percolation and critical percolation in two dimensions" @default.
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• W2107449886 doi "https://doi.org/10.1214/09-aop462" @default.
• W2107449886 hasPublicationYear "2009" @default.
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