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15 Aug 2012: 24 C. BEZUIDENHOUT, G. GRIMMETT, A. LOFFLERwhence, by Wald's equation ([13], p.

15 Aug 2012: THE RANDOM-CLUSTER MODEL. Geoffrey GrimmettAbstra t. The class of random-cluster models is a unification of a variety of sto-chastic processes of significance for probability and statistical physics, including per-colation, Ising, and Potts models;

23 Jul 2012: 1.24) η(ω) = {e E : ω(e) = 1}. Clearly,ω1 ω2 if and only if η(ω1) η(ω2).

15 Aug 2012: CRITICAL PROBABILITIES FOR SITE. AND BOND PERCOLATION MODELS. G. R. Grimmett and A. M. Stacey. Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeAbstract. Any infinite graph G = (V, E) has a site percolation critical

15 Aug 2012: POTTS MODELS AND RANDOM-CLUSTER. PROCESSES WITH MANY-BODY INTERACTIONS. Geoffrey GrimmettAbstra t. Known differential inequalities for certain ferromagnetic Potts models with pair-interactions may be extended to Potts models with many-body

15 Aug 2012: BRANCHING PROCESSES, AND. RANDOM-CLUSTER MEASURES ON TREES. Geoffrey Grimmett, Svante JansonAbstra t. Random-cluster measures on infinite regular trees are studied in con-junction with a general type of ‘boundary condition’, namely an

15 Aug 2012: Mathematics and its Applications, vol. 99, Springer, New York, pp. 1–24.Aizenman, M.

15 Aug 2012: THE RANDOM-CLUSTER MODEL. ON THE COMPLETE GRAPH. Béla Bollobás, Geoffrey Grimmett, Svante JansonAbstract. The random-cluster model of Fortuin and Kasteleyn contains as specialcases the percolation, Ising, and Potts models of statistical physics.

15 Aug 2012: Theorem 6. [24] We have that µp(K = 1) = 1 whenever p > pentc. ... Soc., 130:175–188, 2001. MR1797779. [24] O. Häggström. Uniqueness of the infinite entangled component in three-dimensional bond percolation.

15 Aug 2012: See [24, 51, 52] for more informa-tion and references.Few non-trivial facts are known about the limit set L, and much eort hasbeen spent, largely inconclusively, on attempting to