{
  "id": "2409.08882",
  "version": "v1",
  "published": "2024-09-13T14:48:36.000Z",
  "updated": "2024-09-13T14:48:36.000Z",
  "title": "Quantitative propagation of chaos for non-exchangeable diffusions via first-passage percolation",
  "authors": [
    "Daniel Lacker",
    "Lane Chun Yeung",
    "Fuzhong Zhou"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal law of any subset of particles is compared to a suitably chosen product measure, and we find sharp relative entropy estimates between the two. Building upon prior work of the first author in the exchangeable setting, we use a generalized form of the BBGKY hierarchy to derive a hierarchy of differential inequalities for the relative entropies. Our analysis of this complicated hierarchy exploits an unexpected but crucial connection with first-passage percolation, which lets us bound the marginal entropies in terms of expectations of functionals of this percolation process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-13T14:48:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-passage percolation",
      "quantitative propagation",
      "non-exchangeable diffusions",
      "mean field approximations",
      "suitably chosen product measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}