Rigidity of the interface for percolation and random-cluster models

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dc.creatorGielis, Guy
dc.creatorGrimmett, Geoffrey
dc.date2001-09-17
dc.date.accessioned2026-07-07T04:43:24Z
dc.date.available2026-07-07T04:43:24Z
dc.descriptionWe study conditioned random-cluster measures with edge-parameter p and cluster-weighting factor q satisfying q \ge 1. The conditioning corresponds to mixed boundary conditions for a spin model. Interfaces may be defined in the sense of Dobrushin, and these are proved to be `rigid' in the thermodynamic limit, in three dimensions and for sufficiently large values of p. This implies the existence of non-translation-invariant (conditioned) random-cluster measures in three dimensions. The results are valid in the special case q=1, thus indicating a property of three-dimensional percolation not previously noted.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/0109103
dc.identifierhttp://arxiv.org/abs/math/0109103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62203
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B20, 82B43
dc.titleRigidity of the interface for percolation and random-cluster models
dc.typetext

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