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We study a simple stochastic differential equation that models the dispersionof close heavy particles moving in a turbulent flow. In one and two dimensions,the model is closely related to the one-dimensional stationary Schroedingerequation in a random delta-correlated potential. The ergodic properties of thedispersion process are investigated by proving that its generator ishypoelliptic and using control theory.

Ergodic properties of a model for turbulent dispersion of inertial particles