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To examine how peculiar velocities can affect the two-, three-, and four-point redshift correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize redshift distortions for four different volume-limited samples from each of the GA, SSRS, and IRAS redshift catalogs. We present the results as the correlation length r₀_ and power index γ of the two-point correlations, ξ₀_ᵇar^ = (r₀_/r) gamma, and as the hierarchical amplitudes of the three- and four-point functions, S₃_ = ξ₃_ᵇar^/ξ₂_ᵇar²^ and S₄_ = ξ₄_ᵇar^/ξ₂_ᵇar³^. We find a characteristic distortion for ξ₂_ᵇar^; the slope γ is flatter and the correlation length is larger in redshift space than in real space; that is, redshift distortions "move" correlations from small to large scales. At the largest scales (up to 12 Mpc), the extra power in the redshift distribution is compatible with OMEGA⁴/7^/b ~ 1. We estimate OMEGA⁴/7^/b to be 0. 53 +/- 0. 15, 1. 10 +/- 0. 16, and 0. 84 +/- 0. 45 for the CfA, SSRS, and IRAS catalogs. Higher order correlations ξ₃_ᵇar^ and ξ₄_ᵇar^ suffer similar redshift distortions but in such a way that, within the accuracy of our analysis, the normalized amplitudes S₃_ and S₄_ are insensitive to this effect. The hierarchical amplitudes S₃_ and S₄_ are constant as a function of scale between 1 and 12 Mpc and have similar values in all samples and catalogs, S₃_ ~ 2 and S₄_ ~ 6, despite the fact that ξ₂_ᵇar, ξ₃_ᵇar^ differ from one sample to another by large factors (up to a factor of 4 in ξ₂_ᵇar^, 8 for ξ₃_ᵇar^, and 12 for ξ-4_ᵇar^. The agreement between the independent estimations of S₃_ and S₄_ is remarkable given the different criteria in the selection of galaxies and also the difference in the resulting range of densities, luminosities, and locations between samples.
Fry et al. (Fri,) studied this question.