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 Incoming links: Skewness

Unsmoothed matter-density reduced skewness 2026-10-05

For Gaussian initial conditions and the Einstein-de Sitter second-order standard perturbation theory density kernel, the unsmoothed density contrast obeys

⟨ δ^{3} ⟩ = \frac{34}{7} σ^{4} + O (σ^{6}), σ^{2} = ⟨ δ^{2} ⟩ .

There are three choices of the second-order field and two connected Wick contractions; the angular average of

F_{2}

is

5/7 + (2/7) /3 = 17/21

. Thus the reduced skewness is

6 (17/21) = 34/7

. Smoothing changes this result, and the unsmoothed calculation requires a finite variance.

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