Branching Processes, and Random-Cluster Measures on Trees

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dc.creatorGrimmett, Geoffrey
dc.creatorJanson, Svante
dc.date2004-10-13
dc.date.accessioned2026-07-07T05:13:15Z
dc.date.available2026-07-07T05:13:15Z
dc.descriptionRandom-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?
dc.identifierhttps://arxiv.org/abs/math/0410311
dc.identifierhttp://arxiv.org/abs/math/0410311
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72875
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 60J80, 82B20
dc.titleBranching Processes, and Random-Cluster Measures on Trees
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