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2007 The size of a pond in 2D invasion percolation
Jacob van den Berg, Antal Jarai, Balint Vagvolgyi
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Electron. Commun. Probab. 12: 411-420 (2007). DOI: 10.1214/ECP.v12-1327

Abstract

We consider invasion percolation on the square lattice. van den Berg, Peres, Sidoravicius and Vares have proved that the probability that the radius of a so-called pond is larger than $n$, differs at most a factor of order log $n$ from the probability that in critical Bernoulli percolation the radius of an open cluster is larger than $n$. We show that these two probabilities are, in fact, of the same order. Moreover, we prove an analogous result for the volume of a pond.

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Jacob van den Berg. Antal Jarai. Balint Vagvolgyi. "The size of a pond in 2D invasion percolation." Electron. Commun. Probab. 12 411 - 420, 2007. https://doi.org/10.1214/ECP.v12-1327

Information

Accepted: 26 October 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1128.60087
MathSciNet: MR2350578
Digital Object Identifier: 10.1214/ECP.v12-1327

Subjects:
Primary: 60K35
Secondary: 82B43

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