The hierarchy of correlation functions and its relation to other measures of galaxy clustering.
Abstract
We derive and display relations which can be used to express many quantitative measures of clustering in terms of the hierarchy of correlation functions. The convergence rate and asymptotic behaviour of the integral series which usually result is explored as far as possible using the observed loworder galaxy correlation functions. On scales less than the expected nearest neighbour distance most clustering measures are influenced only by the lowest order correlation functions. On all larger scales their behaviour, in general, depends significantly on correlations of high order and cannot be approximated using the loworder functions. Bhavsar's observed relation between density enhancement and the fraction of galaxies included in clusters is modelled and is shown to be only weakly dependent on highorder correlations over most of its range. The probability that a randomly placed region of given volume be empty is discussed as a particularly simple and appealing example of a statistic which is strongly influenced by correlations of all orders, and it is shown that this probability may obey a scaling law which will allow a test of the smallscale form of highorder correlations.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 January 1979
 DOI:
 10.1093/mnras/186.2.145
 Bibcode:
 1979MNRAS.186..145W
 Keywords:

 Astronomical Models;
 Correlation;
 Galactic Clusters;
 Spatial Distribution;
 Luminous Intensity;
 Mathematical Models;
 Astronomy;
 Galaxy Clustering