= Correlation function
{disambiguate=astronomy}
{title2=$\xi(r)$}
{wiki}
= Cosmological two-point correlation function
{synonym}
The <cosmological two-point correlation function> measures excess pairing or correlated density fluctuations at a separation. For a statistically homogeneous and isotropic mean-zero <density contrast>, $\xi(r)=\langle\delta(\mathbf x)\delta(\mathbf x+\mathbf r)\rangle$. For distinct points in a discrete galaxy population it instead specifies the factorial pair density, $\bar n^2[1+\xi(r)]$. The latter excludes self-pairs; an unsmoothed discrete-density covariance also contains a <Dirac delta> at zero separation. These definitions connect large-scale galaxy clustering with the <matter power spectrum> while keeping <galaxy power spectrum shot noise> separate.
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