{
  "abstract": "We study Bernoulli bond percolation under weak covering maps for a class of weighted inhomogeneous product measures such that each edge $e$ carries a positive weight $w(e)$ and is open at intensity $λ\\geq 0$ with probability $1-\\exp(-λw(e))$. We prove a strict monotonicity of the weighted critical intensities $λ_c$ in the covering compatibility setting under bounded degree, uniform ellipticity, tame fibre and disjoint tree-lifting. While for the weighted uniform connection thresholds $λ_{\\mathrm{conn}}$, we establish their strict monotonicity for non-injective weak covering maps under bounded degree, covering compatibility, uniform ellipticity, bounded-fibre and disjoint tree-lifting. Moreover, we verify a general-profile theorem on strict monotonicities of the two thresholds $λ_c$ and $λ_{\\mathrm{conn}}$ respectively under explicit compact-interval finite-energy, derivative bounds and aforementioned geometric conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22417",
  "author_total": 3,
  "authors": [
    {
      "name": "Jing Liu"
    },
    {
      "name": "Kainan Xiang"
    },
    {
      "name": "Lang Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71gxadzx5cjsn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22417",
  "fulltext_url": null,
  "id": "71gxadzx5cjsn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22417",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222919883",
  "pdf_url": "https://arxiv.org/pdf/2610.22417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71gxadzx5cjsn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Strict monotonicity of weighted inhomogeneous percolation thresholds under covering maps",
  "title_text": "Strict monotonicity of weighted inhomogeneous percolation thresholds under covering maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/71gxadzx5cjsn",
  "venue": "arXiv",
  "versions": []
}