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- W3023933354 abstract "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 $X_t^iin mathbb{T}^d$, and the type $Xi_t^iin {1,ldots,n}$. While $X_t^i$ is a standard (independent) diffusion process, the evolution of the type $Xi_t^i$ is described by pairwise interactions between different particles under a series of chemical reactions described by a chemical reaction network. We prove that, as $N to infty$, 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." @default.
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- W3023933354 date "2020-01-01" @default.
- W3023933354 modified "2023-09-27" @default.
- W3023933354 title "Quantitative Propagation of Chaos in a Bimolecular Chemical Reaction-Diffusion Model" @default.
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- W3023933354 doi "https://doi.org/10.1137/19m1287687" @default.
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