{
  "abstract": "In this paper, we study the Fisher--KPP equation \\[ \\partial_t u = αΔ_{\\TT_{q+1}}u+βu(1-u), \\] on the homogeneous \\((q+1)\\)-regular tree \\(\\TT_{q+1}\\), with \\(q\\geq2\\), for nontrivial, compactly supported radial initial data. We first obtain an explicit representation of the fundamental solution of the corresponding linearized problem, together with sharp two-sided pointwise estimates. These estimates identify the propagation threshold \\[ β>α(\\sqrt q-1)^2 \\] and determine the associated critical speed \\(c_\\ast\\) and decay rate \\(λ_\\ast\\). In this regime, we prove that, for every fixed \\(θ\\in(0,1)\\), the outermost \\(θ\\)-level set satisfies \\[ κ_θ(t) = c_\\ast t-\\frac{3}{2λ_\\ast}\\log t+O(1), \\qquad t\\to\\infty. \\] Therefore, while the branching geometry affects the threshold for propagation and the values of the critical parameters, the classical Bramson factor \\(3/2\\) persists. Our results therefore extend classical propagation and logarithmic-delay phenomena, previously known for one-dimensional continuous and discrete Fisher--KPP models, to homogeneous trees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33805",
  "author_total": 4,
  "authors": [
    {
      "name": "Edagardo Álvarez"
    },
    {
      "name": "Marina Murillo-Arcila"
    },
    {
      "name": "Rodrigo Ponce"
    },
    {
      "name": "Juan C. Pozo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aaehe3znn0rr9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33805",
  "fulltext_url": null,
  "id": "aaehe3znn0rr9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33805",
  "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.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214721086",
  "pdf_url": "https://arxiv.org/pdf/2609.33805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aaehe3znn0rr9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Logarithmic Bramson correction for Fisher--KPP equations on homogeneous trees",
  "title_text": "Logarithmic Bramson correction for Fisher--KPP equations on homogeneous trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/aaehe3znn0rr9",
  "venue": "arXiv",
  "versions": []
}