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

J. van den Berg, D. Kiss, P. Nolin

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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 process converges in some sense to the frozen percolation process introduced by Aldous in [1]. 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 [9].
Original languageEnglish
Pages (from-to)1-11
JournalElectronic Communications in Probability
Volume17
Issue number2
DOIs
Publication statusPublished - 2012

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