{
  "abstract": "The speed v(lambda) of the lambda-biased random walk on a supercritical Galton-Watson tree without leaves is conjectured to be nonincreasing on [0,m), where m is the mean offspring. For non-constant offspring, monotonicity is known only for small bias: lambda <= 1/1160, lambda <= 1/2, and, when every vertex has at least m_1 >= 2 children, lambda <= m_1/(1+sqrt(1-1/m_1)). For offspring uniform on {2,3} (m=2.5) the last bound is 2/(1+sqrt(1/2)) = 1.17157... We prove, with computer assistance, that v is strictly decreasing on [0,1.755] for this law. The proof has three parts. Aidekon's speed formula gives v=(R-lambda)/(R+lambda) for an explicit functional R, so v decreases exactly when R/lambda does; we compare R/lambda at two biases directly, which avoids differentiating the conductance. A pathwise Lipschitz bound on the conductance in lambda turns that comparison into an inequality between expectations of explicit functions. A monotone sandwich of discretised laws gives two-sided bounds on the conductance law, and each lambda-cell is verified with exact rational arithmetic on top of bounded floating-point error; an independent interval-arithmetic implementation re-certifies five cells, including the one that sets the endpoint. The method stops where the crude Lipschitz bound becomes too weak; sharper control of the derivative of the conductance is what the full range needs. Code and certificates are public.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29894",
  "author_total": 2,
  "authors": [
    {
      "name": "Madhulatha Mandarapu"
    },
    {
      "name": "Sandeep Kunkunuru"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezwwbf6qse9nq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29894",
  "fulltext_url": null,
  "id": "ezwwbf6qse9nq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29894",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214323464",
  "pdf_url": "https://arxiv.org/pdf/2609.29894",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezwwbf6qse9nq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.29894",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29894"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Computer-Assisted Proof of Speed Monotonicity for the Biased Random Walk on a Galton-Watson Tree Beyond the Known Range",
  "title_text": "A Computer-Assisted Proof of Speed Monotonicity for the Biased Random Walk on a Galton-Watson Tree Beyond the Known Range",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/ezwwbf6qse9nq",
  "venue": "arXiv",
  "versions": []
}