Search

15 Aug 2012: For A,B Zd, we say that A is connected to B if thereexist a A and b B such that a b; in this case, we write A B. ... We saythat A is fully connected to B if, for all b B, there exists a A such that a b;in this case, we write A fc B.

11 Apr 2012: More generally, for A, B Zdwe write A B (and similarly for the other relations) if a b for some a A and b B. ... B Ax,m(n) = {ρi = ri for 1 i < k} Ax,m(n).

15 Aug 2012: the vector p has distribution given by Pp,(b) if p1 p2 then p1 p2. ... Take a = b = pc(T) for some small positive. Then choose largeenough so that a0 > pc(T).

15 Aug 2012: a b‖ = ‖b c‖ = ‖c d‖ = ‖d a‖ = 1},. ... Lemma 6.8 If 0 < s < t < 1, there exist a = a(s, t) > 0 and b = b(s, t) > 0such that.

15 Aug 2012: Let. (a′,b′) = (a,b) ǫ(cos α, sin α). where ǫ is small and positive. ... a small amount only. Take a = b = pc(T) ζ for some small positive ζ.

23 Jul 2012: µ1(σ) =1. Z Pexp. {β. eEδe(σ). }, σ 6. (b) Marginal on. ... b) Let ω be given. We have that. (1.18). eE. {(1 p)δω(e),0 pδω(e),1δe(σ). } =

15 Aug 2012: Wehave that. pb(i1, j1, i2, j2) =. . . pπi2qj2 if (i1, j1) = (1,b),. ... p,q whenever ′.Part (b) may be extended as follows to arbitrary equivalence relations.

15 Aug 2012: There exists astrictly positive constant b = b(L) such that the number of points y of L satisfyingkyk r does not exceed brd. ... if and only if j!n Bj! j! Bj for every open ball B Rd.

15 Aug 2012: Similarly, for A,B V , we writeA B if there exist a A and b B such that a b. ... Let b = b(x,ψ) denote the number of edges ofE of the form 〈x,z〉 with ψz = 1.

15 Aug 2012: For any ω and any finite box B, we denote by ωB the followingconfiguration:. ... and b,where the symmetric function κN = κN,ω,C is given by.

20 Dec 2012: 2τ 1 E|Ŝn=2 Lθ|:. (b) Let N̂CPSSn,τ = {1,. , p}Ŝ. ... If τ { 12 1=B, 12 3=.2B/, 12 2=B,. , 1}, then.

15 Aug 2012: For A, B V , we write AH B if either A B 6= or there exist a A and b B. ... 0 otherwise,. where A B means that there exists a A ( V ) and b B ( V ) such that a and bare in the same component of the random hypergraph (V, η(

15 Aug 2012: the vector p has distribution given by Pp,(b) if p1 p2 then p1 p2. ... Take a = b = pc(T) for some small positive. Then choose largeenough so that a0 > pc(T).