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

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