The cross-correlation function is a subclass of the two-point correlation function used in case of two different classes of objects (e.g. two types of galaxies from two different surveys in the same volume) and . It defines a (symmetric) probability to find a pair in which is occupied by an object from a first catalogue and by one from the second as

Another definition (see e.g. [1, 2]) can be given in terms of density contrast when considering the objects distributions as continuous functions of density and , the mean values of which are and . In this case: or where the angle brackets indicate an averaging over the sample volume .

The cross-correlation function gives information about the density profile around objects, e.g. between galaxies and clusters measures the average galaxy density profile around clusters, at least out to radii where clusters overlap (see e.g. [2]).

Another definition (see e.g. [1, 2]) can be given in terms of density contrast when considering the objects distributions as continuous functions of density and , the mean values of which are and . In this case: or where the angle brackets indicate an averaging over the sample volume .

The cross-correlation function gives information about the density profile around objects, e.g. between galaxies and clusters measures the average galaxy density profile around clusters, at least out to radii where clusters overlap (see e.g. [2]).