On superdiffusive behavior of a passive tracer in a Poisson shot noise field (Q638663)

The author investigates the trajectory of the passive tracer model generated by the ordinary differential equation \(\mathrm{d}\mathbf{x}(t)/\mathrm{d}t= \mathbf{F}(\mathbf{x}(t)),\) \(\mathbf{x}(0)=\mathbf{x}_{0}\), where \(\mathbf{F} \) is a zero-mean homogeneous isotropic Poisson shot noise random field. The superdiffusive character of the trajectories is proved under suitable conditions on the energy spectrum of the velocity field.