Hydrodynamic limit of particle systems with long jumps

Details Hydrodynamic limit of particle systems with long jumps Hydrodynamic limit of particle systems with long jumps

2008-05-09

arxiv.org/abs/0805.1326v2

Mathematics

Probability

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

Scientific paper

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.

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