{
  "id": "1406.2115",
  "version": "v2",
  "published": "2014-06-09T09:28:12.000Z",
  "updated": "2015-02-14T14:27:01.000Z",
  "title": "Quantitative propagation of chaos for generalized Kac particle systems",
  "authors": [
    "Roberto Cortez",
    "Joaquin Fontbona"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a class of one dimensional particle systems with binary interactions of Bird type, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic economic models. We obtain explicit rates of convergence for the Wasserstein distance between the law of the particles and their limiting law, which are linear in time and depend in a mild polynomial manner on the number of particles. The proof is based on a novel coupling between the particle system and a suitable system of non-independent nonlinear processes, as well as on recent sharp estimates for empirical measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-09T09:28:12.000Z",
      "abstract": "We study a class of one dimensional particle systems with binary interactions of Bird type, which includes Kac's simplified model of the Boltzmann equation and some kinetic models for the evolution of wealth distribution. We obtain explicit rates of convergence, as the total number of particles goes to $\\infty$, for the Wasserstein distance between the law of a particle and its limiting law, which depend linearly on time. The proof is based on a novel coupling between the particle system and a suitable system of non-independent nonlinear processes, as well as on recent sharp estimates for empirical measures.",
      "comment": "21 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-14T14:27:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22",
      "82C40"
    ],
    "keywords": [
      "generalized kac particle systems",
      "quantitative propagation",
      "non-independent nonlinear processes",
      "dimensional particle systems",
      "kacs simplified model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.2115C"
    }
  }
}