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

Jacob van den Berg (Centrum Wiskunde & Informatica (CWI))
Demeter Kiss (Centrum Wiskunde & Informatica (CWI))
Pierre Nolin (ETH Zürich and Courant Institute New York University)

Abstract


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 processconverges in some sense to the frozen percolation process introducedby 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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Pages: 1-11

Publication Date: January 6, 2012

DOI: 10.1214/ECP.v17-1694

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