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Continuity of percolation probability in ∞ + 1 dimensions

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Yu Zhang
Yu Zhang*
Affiliation:
University of Colorado
*
∗Postal address: Department of Mathematics, University of Colorado, Colorado Springs, CO 80933, USA. Supported by a grant from the NSF.
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Abstract

We consider percolation on the graph of the product of a regular tree T with degree d and the line ℤ, in which each tree edge is open with probability 1 – exp(–JTß) and each line edge is open with probability . Let C(o, 0) be the open cluster for . Denote by θ (β) the percolation probability. Here we show that θ (β) is continuous when ß > ßc, where ßc = sup{ß : θ(β) = 0}.

Keywords

PERCOLATIONTREES

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 427 - 433
Copyright
Copyright © Applied Probability Trust 1996 

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References

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