Hydrodynamic limit of particle systems with long jumps
Probability
2009-08-28 v2
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.
Cite
@article{arxiv.0805.1326,
title = {Hydrodynamic limit of particle systems with long jumps},
author = {M. Jara},
journal= {arXiv preprint arXiv:0805.1326},
year = {2009}
}
Comments
Extended version, uniqueness of hydrodynamic equation and general initial profiles added