{
  "id": "2308.04174",
  "version": "v1",
  "published": "2023-08-08T10:13:23.000Z",
  "updated": "2023-08-08T10:13:23.000Z",
  "title": "The parametrix construction of the heat kernel on a graph",
  "authors": [
    "Gautam Chinta",
    "Jay Jorgenson",
    "Anders Karlsson",
    "Lejla Smajlović"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP",
    "math.CO"
  ],
  "abstract": "In this paper we develop the parametrix approach for constructing the heat kernel on a graph $G$. In particular, we highlight two specific cases. First, we consider the case when $G$ is embedded in a Eulidean domain or manifold $\\Omega$, and we use a heat kernel associated to $\\Omega$ to obtain a formula for the heat kernel on $G$. Second, we consider when $G$ is a subgraph of a larger graph $\\widetilde{G}$, and we obtain a formula for the heat kernel on $G$ from the heat kernel on $\\widetilde{G}$ restricted to $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-08T10:13:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K08",
      "05C50",
      "35K05",
      "39A12",
      "33C10"
    ],
    "keywords": [
      "heat kernel",
      "parametrix construction",
      "parametrix approach",
      "eulidean domain",
      "larger graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}