Hydrodynamic limit of particle systems with long jumps

Abstract

We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat equation. The scaling in this case is superdiffusive. In addition, we discuss a central limit theorem for a tagged particle on the zero-range process and existence and uniqueness of solutions of the Cauchy problem for the fractional heat equation.

Extended version, uniqueness of hydrodynamic equation and general initial profiles added

References in corpus (1)

• Stochastic interacting particle systems out of equilibrium

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