{
  "abstract": "We prove that on Z^d , with d> 6, and under the usual assumption that the two-point function and the Green's function are of the same order, the probabilities to hit any finite set for a critical Branching random walk starting from the origin and the critical percolation cluster of the origin are within a positive multiplicative constant one from each other, as long as the set is sufficiently far away from the origin comparatively to its diameter. The proof relies on the introduction of a truncated equilibrium measure in percolation and the derivation of an approximate last passage formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37133",
  "author_total": 1,
  "authors": [
    {
      "name": "Bruno Schapira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2c802tc367t4j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37133",
  "fulltext_url": null,
  "id": "2c802tc367t4j",
  "issns": [],
  "landing_url": "https://hal.science/hal-05838269v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7224088415",
  "pdf_url": "https://hal.science/hal-05838269/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2c802tc367t4j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05838269",
      "source": "hal",
      "url": "https://hal.science/hal-05838269v1"
    },
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37133",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37133"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "High-dimensional critical percolation and critical Branching random walks are intersection equivalent",
  "title_text": "High-dimensional critical percolation and critical Branching random walks are intersection equivalent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2c802tc367t4j",
  "venue": "HAL",
  "versions": []
}