  We obtain an implicit equation for the correlation dimension of dynamical
systems in terms of an integral over a propagator. We illustrate the utility of
this approach by evaluating the correlation dimension for inertial particles
suspended in a random flow. In the limit where the correlation time of the flow
field approaches zero, taking the short-time limit of the propagator enables
the correlation dimension to be determined from the solution of a partial
differential equation. We develop the solution as a power series in a
dimensionless parameter which represents the strength of inertial effects.
