The size of a pond in 2D invasion percolation

Antal Jarai, Jacob van den Berg, Balint Vagvolgyi

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.
Original languageEnglish
Article number39
Pages (from-to)411-420
Number of pages10
JournalElectronic Communications in Probability
Volume12
DOIs
Publication statusPublished - 2007

Keywords

  • invasion percolation, pond, critical percolation

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