Abstract
Modify the usual percolation process on the infinite binary tree by forbidding infinite
clusters to grow further. The ultimate configuration will consist of both infinite and
finite clusters. We give a rigorous construction of a version of this process and show
that one can do explicit calculations of various quantities, for instance the law of the
time (if any) that the cluster containing a fixed edge becomes infinite. Surprisingly, the
distribution of the shape of a cluster which becomes infinite at time
t > ½ does not depend on t; it is always distributed as the incipient infinite percolation cluster on the
tree. Similarly, a typical finite cluster at each time t > ½ has the distribution of a critical
percolation cluster. This elaborates an observation of Stockmayer [12].
Publisher
Cambridge University Press (CUP)
Cited by
25 articles.
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