Search

15 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).

15 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].

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;

15 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.

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: 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: Our basic strategy in proving the central limit theorem isto adapt the arguments proposed by Kipnis and Varadhan [24] and further developed byDeMasi, Ferrari, Goldstein, and Wick [10, 11]. ... One of the main properties of the chain Xω is its

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