SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2098-2133, January 2020.
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 $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in \{1,\ldots,n\}$. 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.

中文翻译：

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双分子化学反应扩散模型中混沌的定量传播

SIAM数学分析杂志，第52卷，第2期，第2098-2133页，2020年1月。
我们研究了一种由N相互作用的粒子组成的随机系统，该系统模拟了双分子化学反应-扩散。在此模型中，每个粒子$ i $都具有两个属性：\ mathbb {T} ^ d $中的空间位置$ X_t ^ i \，和\ {1，\ ldots，n \中的类型\\ Xi_t ^ i \ } $。虽然$ X_t ^ i $是标准的（独立的）扩散过程，但是$ \ Xi_t ^ i $类型的演化是通过化学反应网络描述的一系列化学反应下不同粒子之间的成对相互作用来描述的。我们证明，当$ N \ infty $时，随机系统具有一个平均场极限，该极限由一个非局部反应扩散偏微分方程描述。特别是，我们获得了相互作用粒子系统的混沌结果的定量传播。我们的证明是基于Jabin和Wang [Invent。数学，214（2018），523--591页]。相对熵方法的关键要素是对特殊分区函数的大偏差估计，该估计先前已通过组合估计得到证明。我们基于一种新颖的mar论证给出了一个简单的概率证明。