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13 Sep 2012: K}. We aim to minimise the misclassification error rate orrisk :. Risk(C) = P(. C(X) 6= Y). September 13, 2012- 24. R.

15 Aug 2012: mains unproved. Using Theorem 4.2 and an argument of Zhang (see [24, p. ... Related Fields 92, 511–527. 24. Grimmett, G. R. (1989), Percolation, Springer–Verlag, Berlin.

20 Apr 2012: 24. (5.19). Hence the number of rounds before hitting the root has a Geometric distribution,so it has bounded expectation. ... 1. α2β(n1)1lk=2. Po(Zn, > 0,Zn,k > 0). (5.24). 25. We let An, = Jn,1 Jn, Jn,1, for = 1, ,α2β(n1) 1 and for = 0 we

15 Aug 2012: min h, max h] =. [. 12,. 12. ]. (24). For a general unbiased walk, we take ascoin flip the unitary matrix. ... We have as beforethat the domain of the limit distribution is asin (24).

15 Aug 2012: Whenq = 2, this role is played by the Simon{Lieb inequality (see [24, 27]). ... 1986). Phase coexistence and surface tensions for the Pottsmodel. Communications in Mathematical Physics 105, 527{545.24.

15 Aug 2012: F., Percolation theory and some. applications, Itogi Nauki i Techniki (Series of Probability Theory, Mathematical Statistics,Theoretical Cybernetics) 24 (1986), 53–110.

15 Aug 2012: 24] for a discussion). If d 3 and q is sufficiently large, then the uniqueness is aconsequence of Pirogov–Sinai theory ([37, 39]). ... 1992). Potts models and random-cluster processes with many-body interac-. tions (to appear).24.

2 Jul 2012: Probab. 24 (1996), 1036–1048. 4. M. Atapour and N. Madras, On the number of entangled clusters, J.Statist. ... J. Probab. Stat. 24 (2010), 300–320. 114. H. Kesten, V. Sidoravicius, and Y.

15 Aug 2012: θΛ(p, q) = φΛ,p,q(A). (24). It is not hard to see that.

15 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