GALAXY CORRELATIONS, COUNTS, AND MOMENTS

We explore relations among galaxy correlation functions, counts, moments, and fractal dimensions. Using counts, or factorial moments in cells of variable size, one can conveniently test for possible scaling behavior. Exact relations between (cell-averaged) density moments F(p) and cumulant moments K(p) are given, suggesting alternative methods to investigate the texture of galaxy distributions. In particular, one can systematically extract the sequence of cumulant moments from these identities. Specializing to translation invariance and scaling, many simplifications occur. The hierarchical, or linked pair approximation expressing higher order cumulations in terms of products of two particle cumulants lead to several interesting results. This hypothesis is shown to be closely connected to the negative binomial distribution, when suitable coefficients are chosen. Remarkably, the same correlation structures (although with distinct correlation functions) seem to work for hadronic multiplicity distributions in high-energy collisions, and for galaxies.