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notes.dvi
www.statslab.cam.ac.uk/~grg/papers/USrednotes.pdf15 Aug 2012: PERCOLATION ANDDISORDERED SYSTEMSGeorey GRIMMETT. 2PREFACEThis course aims to be a (nearly) self-contained account of part of the mathematicaltheory of percolation and related topics. The rst nine chapters summarise rigorousresults in percolation -
rctree.dvi
www.statslab.cam.ac.uk/~grg/papers/USrctree.pdf15 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 -
rcproc.dvi
www.statslab.cam.ac.uk/~grg/papers/USrcproc.pdf15 Aug 2012: φbp,q = αφ′ (1 α)φ′′. for some distinct φ′,φ′′ Rp,q. It follows by [24, Thm. ... The given statement for θ0 may be proved similarly, making use of Theorem3.2 and [24, Prop. -
potts2.dvi
www.statslab.cam.ac.uk/~grg/papers/USpotts2.pdf15 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 -
pinball.dvi
www.statslab.cam.ac.uk/~grg/papers/USpinball.pdf15 Aug 2012: Rotator pin-ball. Ruijgrok and Cohen [24] have proposed a general studyof mirror and rotator' models. ... Quas, A., Some properties of Lorentz lattice gas models (1996) (to appear).24. -
opt.dvi
www.statslab.cam.ac.uk/~grg/papers/USopt.pdf15 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 -
meanf.dvi
www.statslab.cam.ac.uk/~grg/papers/USmeanf.pdf15 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. -
mcst.dvi
www.statslab.cam.ac.uk/~grg/papers/USmcst.pdf15 Aug 2012: 24 C. BEZUIDENHOUT, G. GRIMMETT, A. LOFFLERwhence, by Wald's equation ([13], p. -
keane.dvi
www.statslab.cam.ac.uk/~grg/papers/USkeane.pdf15 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. -
inter4.dvi
www.statslab.cam.ac.uk/~grg/papers/USinter4.pdf15 Aug 2012: Using (5.17)–(5.18) of[22], together with estimates at the beginning of the proof of Lemma (2.24) of [29],we find that. ... We have forf W(δ1) QG/3(e1) that. τ[QG/3(f) EL1,M1. ]= QG/3(τf) EL2,M2, (24).
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