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- W2950881429 abstract "Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of random-cluster measures are explored for certain classes of equivalence relations. In proving uniqueness, the following problem concerning branching processes is encountered and answered. Consider bond percolation on the family-tree $T$ of a branching process. What is the probability that every infinite path of $T$, beginning at its root, contains some vertex which is itself the root of an infinite open sub-tree?" @default.
- W2950881429 created "2019-06-27" @default.
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- W2950881429 date "2004-10-13" @default.
- W2950881429 modified "2023-09-27" @default.
- W2950881429 title "Branching Processes, and Random-Cluster Measures on Trees" @default.
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