SUMMARY
Suppose that there exist C1, c1 > 0, ∈ such that e ρ(ns) c1 ρ(ns) (0 ↔ ns) ≤ C 1 ψ(ns)e Then, for any β and amp;lt; β, there exist C2, c2 > 0 such that e ρ(ns) β (0 ↔ ns) ≤ C 2 ψ(ns)e c2 ρ(ns) -1+η log n Proof. Using, one has that for any κ > 0 and x ∈ Zd, β 0 ↔ x, |C 0 | ≥ f (x) ≤C β 0 ↔ x e -cκρ(x) so, using the assumption, et·ns β 0 ↔ ns, |C0 | ≥ f (ns) ≤ ψ(ns)on for κ large enough. There exist C and amp;lt; ∞, c > 0 such that, for any x . . .
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