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We introduce two discrete models of a collection of colliding particles withstored momentum and study the asymptotic growth of the mean-square displacementof an active particle. We prove that the models are superdiffusive in onedimension (with power law correction) and diffusive in three and higherdimensions. In two dimensions we demonstrate superdiffusivity (with logarithmiccorrection) for certain anisotropic initial conditions.

Diffusion and superdiffusion in lattice models of colliding particles with stored momentum