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The relation between the galaxy correlation function in real andredshift-space is derived in the linear regime by an appropriate averaging ofthe joint probability distribution of density and velocity. The derivationrecovers the familiar linear theory result on large scales but has theadvantage of clearly revealing the dependence of the redshift distortions onthe underlying peculiar velocity field; streaming motions give rise todistortions of ${\cal O}(\Omega^{0.6}/b)$ while variations in the anisotropicvelocity dispersion yield terms of order ${\cal O}(\Omega^{1.2}/b^2)$. Thisprobabilistic derivation of the redshift-space correlation function is similarin spirit to the derivation of the commonly used ``streaming'' model, in whichthe distortions are given by a convolution of the real-space correlationfunction with a velocity distribution function. The streaming model is oftenused to model the redshift-space correlation function on small, highlynon-linear, scales. There have been claims in the literature, however, that thestreaming model is not valid in the linear regime. Our analysis confirms thisclaim, but we show that the streaming model can be made consistent with lineartheory {\it provided} that the model for the streaming has the functional formpredicted by linear theory and that velocity distribution is chosen to be aGaussian with the correct linear theory dispersion.Comment: 14 pages, no figures, uuencoded compressed postscrip

On the Validity of the Streaming Model for the Redshift-Space Correlation Function in the Linear Regime