{
  "abstract": "We consider a drainage network model represented by a system of coalescing random walks exhibiting long range dependence before coalescence. This model was introduced by Gangopadhyay et. al. [GRS04] and Coletti et. al. [CFD09] proved its convergence to the Brownian web under diffusive scaling. Santos et. al. [SVZ24] considered a branching version of this model where branching occurs with low probabilities varying with the scaling parameter and showed that any sub-sequential limit contains a copy of the Brownian net. It was conjectured that the limit is indeed the Brownian net. In this work we prove this conjecture. Further, compared to [SVZ24], we explore the question of scaling limit in a wider spectrum of scaling regime. This work contributes to the broader understanding of the basin of attraction of the Brownian net.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40555",
  "author_total": 2,
  "authors": [
    {
      "name": "Krishnamurthi Ravishankar"
    },
    {
      "name": "Kumarjit Saha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqvjjjkpxmgen.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40555",
  "fulltext_url": null,
  "id": "eqvjjjkpxmgen",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40555",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40555",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eqvjjjkpxmgen.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40555",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40555"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence of a drainage network model with branching to the Brownian net",
  "title_text": "Convergence of a drainage network model with branching to the Brownian net",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/eqvjjjkpxmgen",
  "venue": "arXiv",
  "versions": []
}