ALEX 2018 Workshop: Abstracts

Hydrodynamic limit and large deviations of reaction-diffusion master equations

Markus Mittnenzweig

Weierstraß-Institut Berlin (Germany)

In this talk, I will present a stochastic reaction-diffusion process on a lattice, that combines an exclusion process with the chemical master equation. Particles randomly jump between neighboring lattice sites and can react with each other, when they find themselves at the same lattice position. If the associated chemical reaction network has a detailed-balance equiIibrium, then the hydrodynamic limit of the reaction-diffusion process is given by a reaction-diffusion PDE system with a modified mass-action kinetics. The proof uses the entropy method of Guo, Papanicolaou, and Varadhan. The second part concerns dynamic large deviations from the hydrodynamic limit. I will show the large deviations upper bound and, following [2], make the connection between the rate functional and an entropic gradient structure for the reaction-diffusion PDE system.

References

  • 1 M. Mittnenzweig, Hydrodynamic limit and large deviations of reaction-diffusion master equations, WIAS Preprint No. 2521 (2018).
  • 2 A. Mielke, M. A. Peletier, D. R. M. Renger, On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion Potential Analysis 41 (2014), 1293–1327.