{
  "id": "2106.14000",
  "version": "v1",
  "published": "2021-06-26T11:15:55.000Z",
  "updated": "2021-06-26T11:15:55.000Z",
  "title": "Gibbs point processes on path space: existence, cluster expansion and uniqueness",
  "authors": [
    "Alexander Zass"
  ],
  "comment": "31 pages, 5 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to $\\mathbb{R}^d$, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-26T11:15:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "path space",
      "infinite-volume gibbs point process",
      "cluster expansion tools",
      "explicit activity domain",
      "uniqueness holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}