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Random-cluster representation of the Blume–Capel model B. T. Graham,…
www.statslab.cam.ac.uk/~grg/papers/blume.pdf15 Aug 2012: limΛLd. φ0Λ(A B) = Φ0(1A(ψ)µ0ψ(B)). (7.7). 24 B. T. Graham and G. -
Three theorems in discrete random geometry
www.statslab.cam.ac.uk/~grg/papers/PS_2011_185-rev.pdf27 Jan 2012: gular and hexagonal lattices, [24],(c) the critical point of the random-cluster model on the square lattice with. ... 6See also [51]. Three theorems in discrete random geometry 315. Theorem 3.4 ([24]). -
10-grg.dvi
www.statslab.cam.ac.uk/~grg/books/hammfest/10-grg.pdf15 Aug 2012: F. (1986). Percolation. theory and some applications. Itogi Nauki i Techniki, Series of ProbabilityTheory, Mathematical Statistics, Theoretical Cybernetics, 24, 53–110. -
entperc.dvi
www.statslab.cam.ac.uk/~grg/papers/USentperc.pdf15 Aug 2012: Et(ΨA) aΛs(A) b. for every increasing cylinder event A. Here are some remarks about these two lemmas, which are essentially equa-tions (13.24) and (13.25) of [7]. -
elec.dvi
www.statslab.cam.ac.uk/~grg/papers/USelec.pdf15 Aug 2012: 2.24) x = f (x). As is well known (see Harris (1963) proof of Theorem I.6.1) the only solutions of(2.24) in [0, 1] are q and 1. ... 24 GEOFFREY GRIMMETT AND HARRY KESTEN. as n. Proof. We prove. -
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. -
crit6.dvi
www.statslab.cam.ac.uk/~grg/papers/UScrit6.pdf15 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 -
notes.dvi
www.statslab.cam.ac.uk/~grg/papers/USstflour.pdf15 Aug 2012: PERCOLATION ANDDISORDERED SYSTEMS. Georey 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
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