Author:
GRIMMETT GEOFFREY R.,HOLROYD ALEXANDER E.,KOZMA GADY
Abstract
AbstractTwo related issues are explored for bond percolation on ${\mathbb{Z}^d$ (with d ≥ 3) and its dual plaquette process. Firstly, for what values of the parameter p does the complement of the infinite open cluster possess an infinite component? The corresponding critical point pfin satisfies pfin ≥ pc, and strict inequality is proved when either d is sufficiently large, or d ≥ 7 and the model is sufficiently spread out. It is not known whether d ≥ 3 suffices. Secondly, for what p does there exist an infinite dual surface of plaquettes? The associated critical point psurf satisfies psurf ≥ pfin.
Publisher
Cambridge University Press (CUP)
Cited by
8 articles.
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