A percolation process on the binary tree where large finite clusters are frozen

Details A percolation process on the binary tree where large finite clusters are frozen A percolation process on the binary tree where large finite clusters are frozen

2011-05-10

arxiv.org/abs/1105.1977v1

Mathematics

Probability

11 pages

Scientific paper

We study a percolation process on the planted binary tree, where clusters freeze as soon as they become larger than some fixed parameter N. We show that as N goes to infinity, the process converges in some sense to the frozen percolation process introduced by Aldous. In particular, our results show that the asymptotic behaviour differs substantially from that on the square lattice, on which a similar process has been studied recently by van den Berg, de Lima and Nolin.

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