Scaling Behavior in a Stochastic Self-Gravitating System

A system of stochastic differential equations for the velocity and density of classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling behavior, associated with physically admissible fixed points of the renormalization-group equations, is established. Their regions of stability are identified and the corresponding scaling dimensions are calculated in the one-loop approximation (first order of the $\epsilon$ expansion). The velocity and density fields have independent scaling dimensions. Our analysis supports the importance of the rotational (nonpotential) components of the velocity field in the formation of those scaling laws.