p(ξ1) for a field with N = 32 grid points and a Gaussian power spectrum with Lk0 = 80. The black curve is from simulations, the blue dot-dashed curve shows the best-fitting Gaussian, and the other two curves show the quasi-Gaussian approximation using a constant covariance matrix (green dotted curve) and incorporating its ξ0-dependence (red dashed curve).
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