The size of a pond in 2D invasion percolation

Details The size of a pond in 2D invasion percolation The size of a pond in 2D invasion percolation

2007-08-31

arxiv.org/abs/0708.4369v1

Electron. Comm. Probab. 12 (2007), 411-420

Mathematics

Probability

11 pages

Scientific paper

We consider invasion percolation on the square lattice. It has been proved by van den Berg, Peres, Sidoravicius and Vares, 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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