{
  "annotation_id": "09bc5ede-8321-4cd4-944e-a719fc351b29",
  "date_created": "2026-02-17T05:53:24.274000Z",
  "date_modified": "2026-02-17T05:53:24.274000Z",
  "file_hash": "13a6d8b839f3afbdcad8ccd000cc2c7d50d4caeca06cac6a2064062959b1d47e",
  "private": false,
  "record": {
    "abstract": "For any infinite, connected, locally finite graph $G=(V,E)$, any parameter $p\u003ep^{\\mathrm{site}}_{c}(G)$, and any (finite or infinite) set of vertices $S\\subset V$, we derive explicit exponential-type upper bounds on the disconnection probability $\\mathbb{P}_{p}(S\\nleftrightarrow\\infty)$. The estimates are expressed in terms of a packing profile of $S$, encoded by a $(p,\\varepsilon,c)$--packing number, which counts how many well-separated vertices in $S$ exhibit controlled local-to-global connectivity. The proof combines a local functional characterization of $p^{\\mathrm{site}}_{c}$ from \\cite{ZL24,ZL26} with a packing construction and an amplification-by-independence argument, in the direction of Problem~1.6 in \\cite{DC20}.",
    "arxiv_id": "2601.09950",
    "authors": [
      "Zhongyang Li"
    ],
    "categories": [
      "math.PR",
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Quantitative Supercritical Bounds for Disconnection in Bernoulli Site Percolation",
    "url": "https://arxiv.org/abs/2601.09950",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1471d47a-bd87-472e-8c0b-ef9f031a7e2d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}