{
  "id": "2202.02766",
  "version": "v1",
  "published": "2022-02-06T12:31:31.000Z",
  "updated": "2022-02-06T12:31:31.000Z",
  "title": "Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime",
  "authors": [
    "Efe Onaran",
    "Omer Bobrowski",
    "Robert J. Adler"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-06T12:31:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60F05",
      "60D05",
      "05C80"
    ],
    "keywords": [
      "functional central limit theorems",
      "spatial birth-death processes",
      "thermodynamic regime",
      "local statistics",
      "random geometric graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}