{
  "id": "1906.01051",
  "version": "v1",
  "published": "2019-06-03T19:58:19.000Z",
  "updated": "2019-06-03T19:58:19.000Z",
  "title": "Quantitative Propagation of Chaos in the bimolecular chemical reaction-diffusion model",
  "authors": [
    "Tau Shean Lim",
    "Yulong Lu",
    "James Nolen"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "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 $X_t^i\\in \\mathbb{T}^d$, and the type $\\Xi_t^i\\in \\{1,\\cdots,n\\}$. 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 in the large particle limit the stochastic dynamics converges to 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 \\cite{JW18}. The key ingredient of the relative entropy method is a large deviation estimate for a special partition function, which was proved previously by technical combinatorial estimates. We give a simple probabilistic proof based on a novel martingale argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T19:58:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bimolecular chemical reaction-diffusion model",
      "quantitative propagation",
      "relative entropy method",
      "nonlocal reaction-diffusion partial differential equation",
      "mean field limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}