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.
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