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14 Mar 2012: P (Tisol > t) = exp. (c̃d. t. Ψd(t)(1 o(1)). )? (24). Peres et al. [14] and Peres and Sousi [15] studied the detection time for the case when u also ... ClearlyTnonperc Tisol. We conclude with the question below. Question. Do the tail probabilities of

15 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.

6 Mar 2012: r. Lr. 2j n.(24). If r = , for p0 and bounded, there exists a constant L such that for all jsatisfying 2j j < n we have. ... PROOF. Since Bα = W2α in [24] and it also equals a constant times Rα in [32],this proposition simply combines Theorem 2.1 in

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

15 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.

15 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

20 Apr 2012: E [vol (Wg(t))] c E [vol (W0(t))]. (7). The expected volume of the Wiener sausage with g 0 is known to satisfy [24, 2]. ... P [Kct ] t exp(c1L). (24). We will now derive an upper bound for P[H̃t].

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

10 Nov 2012: ISSN: 1525-2027. Copyright 2006 by the American Geophysical Union 1 of 24. ... GeochemistryGeophysicsGeosystems G3G3 poore et al.: neogene overflow of ncw 10.1029/2005GC001085. 4 of 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.