Dispersion of particle systems in Brownian flows

The authors study the dispersion of a collection of particles carried by an isotropic Brownian flow in ℝ’àd. Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. The authors use estimates for the pair separation process to give a fairly complete picture of this behavior as t⇒•. In particular, for incompressible flows in two dimensions, they show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.