{
  "id": "2304.10298",
  "version": "v1",
  "published": "2023-04-20T13:26:51.000Z",
  "updated": "2023-04-20T13:26:51.000Z",
  "title": "Visibility in Brownain interlacements, Poisson cylinders and Boolean models",
  "authors": [
    "Yingxin Mu",
    "Artem Sapozhnikov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study visibility inside the vacant set of three models in $\\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Boolean model. For each of them, we obtain sharp asymptotic bounds on the probability of visibility to distance $r$ in some direction in terms of the probability of visibility to distance $r$ in a given direction. In dimensions $d\\geq 4$, the ratio of the two probabilities has the same scaling $r^{2(d-1)}$ for all three models, but in lower dimensions the scalings are different. In particular, we improve some main results from arXiv:0905.4874 and arXiv:1709.09052.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-20T13:26:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "poisson cylinders",
      "boolean model",
      "brownain interlacements",
      "sharp asymptotic bounds",
      "study visibility inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}