WIAS Preprint No. 2521, (2018)

Hydrodynamic limit and large deviations of reaction-diffusion master equations



Authors

  • Mittnenzweig, Markus

2010 Mathematics Subject Classification

  • 60F10 35K57 82C35 82C22

Keywords

  • Reaction-diffusion master equation, hydrodynamic limit, large deviations, interacting particle systems

DOI

10.20347/WIAS.PREPRINT.2521

Abstract

We derive the hydrodynamic limit of a reaction-diffusion master equation, that combines an exclusion process with a reversible chemical master equation expression for the reaction rates. The crucial assumption is that the associated macroscopic reaction network has a detailed balance equilibrium. The hydrodynamic limit is given by a system of reaction-diffusion equations with a modified mass action law for the reaction rates. We provide the upper bound for large deviations of the empirical measure from the hydrodynamic limit.

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