# Quantitative propagation of chaos in a bimolecular chemical reaction-diffusion model

Published

Journal Article

© 2020 Society for Industrial and Applied Mathematics. We study a stochastic system of N interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle i carries two attributes: the spatial location Xit ∈ Td, and the type [I]it ∈ { 1, . . ., n} . While Xit is a standard (independent) diffusion process, the evolution of the type [I]it is described by pairwise interactions between different particles under a series of chemical reactions described by a chemical reaction network. We prove that, as N → ∞, the stochastic system has a mean field limit which is described by a nonlocal reaction-diffusion partial differential equation. In particular, we obtain a quantitative propagation of chaos result for the interacting particle system. Our proof is based on the relative entropy method used recently by Jabin and Wang [Invent. Math., 214 (2018), pp. 523-591]. The key ingredient of the relative entropy method is a large deviation estimate for a special partition function, which was proved previously by combinatorial estimates. We give a simple probabilistic proof based on a novel martingale argument.

### Full Text

### Duke Authors

### Cited Authors

- Lim, TS; Lu, Y; Nolen, JH

### Published Date

- January 1, 2020

### Published In

### Volume / Issue

- 52 / 2

### Start / End Page

- 2098 - 2133

### Electronic International Standard Serial Number (EISSN)

- 1095-7154

### International Standard Serial Number (ISSN)

- 0036-1410

### Digital Object Identifier (DOI)

- 10.1137/19M1287687

### Citation Source

- Scopus