Search

15 Aug 2012: It is evident. PERCOLATION AND MINIMAL SPANNING TREES 5from the usual re-scaling argument that(3.2) Pp () = P1 (p1=d)in the case of the Poisson model; see [14], [20] ... Using standard arguments from percolationtheory (see [10], [20]), we have that there

15 Aug 2012: Harris, T. E., A lower bound for the critical probability in a certain percolation process,Proceedings of the Cambridge Philosophical Society 56 (1960), 13{20.7.

9 Jan 2012: Ann. Appl. Probab. 20 462–494. MR2650039[12] TUCKER, A. W. (1946). Some topological properties of disk and sphere.

11 Apr 2012: gx,mp (r) = Pp(x Lr in Rm), gp(r) = Pp(0 Lr ). and. hmp (r) = max{gx,mp (r): x Rm L. }. (20). ... hmp (r) gp(r) as m. (21). By (20), hmp (r) is the maximum of a finite set of polynomials in p.

15 Aug 2012: 724, Springer-Verlag, Berlin.Grimmett, G. R. (1989). Percolation. Springer-Verlag, Berlin. 20 J.

15 Aug 2012: We haveby (20) that. log. (Z1(δ). Z1(EL,M ). )=. eE(δ)EL,M. fp(e,δ,L,M) (21). ... not 0-connected. 20 Guy Gielis and Geoffrey Grimmett. (ix) The projection π(W) of any wall W contains at least one plaquette of δ0.

15 Aug 2012: See [18, 20].] We now repeat the slab argument presented above,and (3.3) follows immediately. ... Using arguments of percolation theory (see [1, 20, 27]), we may show the following.

27 Jan 2012: It may be checked (or see [20, Sect.11.9]) that the families. {. ... The critical surfaces of the above models are given explicitly in [20, 38].

15 Aug 2012: d. dplog µp,q(Ix). 1. p(1 p). f: fx. µp,q(f is open), (5.20). ... 20 B. T. Graham and G. R. Grimmett. (iii) {ψy : ψ B} if x is isolated in ωf, and(iv) B, if both x and y are isolated in ωf.

15 Aug 2012: 6.20) lim infn. P(|Θn θ| < ω(n)1. )> 0. For such θ there exist, by Lemma 6.1 and Theorem 5.1, sequences m,j,k, l ... 20 BÉLA BOLLOBÁS, GEOFFREY GRIMMETT, SVANTE JANSON. Theorem 8.3. Assume λ,q > 0.(a) For any closed subset F of R,.