Electronic Communications in Probability

The size of a pond in 2D invasion percolation

Jacob van den Berg, Antal Jarai, and Balint Vagvolgyi

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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.

Article information

Electron. Commun. Probab. Volume 12 (2007), paper no. 39, 411-420.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

invasion percolation pond critical percolation

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van den Berg, Jacob; Jarai, Antal; Vagvolgyi, Balint. The size of a pond in 2D invasion percolation. Electron. Commun. Probab. 12 (2007), paper no. 39, 411--420. doi:10.1214/ECP.v12-1327. http://projecteuclid.org/euclid.ecp/1465224982.

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