DYNAMICS AND STATISTICS

This chapter studies how the n-point correlation functions have proved useful not only as descriptive statistics but also as dynamic variables in the Newtonian theory of the evolution of clustering. It generalizes the functions to mass correlation functions in position and momentum, and derives the BBGKY hierarchy of equations for their evolution. This yields a new way to analyze the evolution of mass clustering in an expanding universe. Of course, the main interest in the approach comes from the thought that the observed galaxy correlation functions may yield useful approximations to the mass correlation functions, so the observations may provide boundary values for the dynamical theory of evolution of the mass correlation functions. The test will be whether one can find a consistent theory for the joint distributions in galaxy positions and velocities.