Hydrodynamic limit and large deviations of reaction-diffusion master equations
- Mittnenzweig, Markus
2010 Mathematics Subject Classification
- 60F10 35K57 82C35 82C22
- Reaction-diffusion master equation, hydrodynamic limit, large deviations, interacting particle systems
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.