## Flux Large Deviations

### With Robert Patterson (Weierstrass Institute, Berlin)

# Flux Large Deviations

I will present an approach to proving a pathwise large deviations principle for pure jump interacting particle models of chemical reactions in the hydrodynamic limit. I will show that working with the reaction fluxes as well as the reactant concentrations leads to an explicit rate function, from which existing results can be recovered and even strengthened by applying the contraction principle. The proof has two main technical components—a stochastic tilting argument (change of measure) and an analytic approximation argument. These two steps are in a general sense standard, but their managing their interplay is key to avoiding awkward technical assumptions, which we are able to do with the help of a continuity assumption on the initial condition.

If the chemical reaction network can be brought into detailed balance the large deviations rate function can be used to define a canonical gradient flow for the limiting system and thus give a rigorous derivation of the thermodynamic free energy. However, the proof does not require any form of reversibility and so I will make some comments about ongoing work to extend the result to systems of coagulating particles, where the infinite number of possible sizes for an single particle makes the topological questions and analytic approximation argument more delicate.

Joint work with Michiel Renger

- Speaker: Robert Patterson (Weierstrass Institute, Berlin)
- Tuesday 07 May 2019, 14:00–15:00
- Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
- Series: Probability; organiser: Perla Sousi.