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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 39 open journal systems 


The size of a pond in 2D invasion percolation

Jacob van den Berg, CWI and Vrije Universiteit
Antal A. Jarai, Carleton University
Balint Vagvolgyi, Vrije Universiteit


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.


Full text: PDF

Pages: 411-420

Published on: October 26, 2007
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Electronic Communications in Probability. ISSN: 1083-589X