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Proposition 16 ([Uniform second moment]). After fixing the cutoffs as above, there is a constant C_v<∞ such that, for all sufficiently small densities and sufficiently large volumes at each density, ∫f^2μ≤C_v. The constant is uniform for …

Proposition 16 ([Uniform second moment]). After fixing the cutoffs as above, there is a constant C_v<∞ such that, for all sufficiently small densities and sufficiently large volumes at each density, ∫f^2μ≤C_v. The constant is uniform for ρ/2≤N/V≤2ρ and 0<T≤ρ² .