{
  "abstract": "The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a paradigmatic example of front propagation and asymptotic-state selection. Using a unified renormalization-group (RG) framework, we show that its traveling-wave solutions form a continuous family of RG fixed points and that all fronts with v >= 2 are locally RG-stable. The resulting RG stability criterion reproduces the classical linear-stability analysis of Canosa, according to which all fronts with v >= 2 are stable. Nevertheless, the asymptotically selected front is v=2, determined by the leading-edge structure of the initial condition rather than by RG stability. The FKPP equation thus provides an explicit example in which RG fixed-point stability does not determine asymptotic-state selection, demonstrating that stability and selection constitute distinct aspects of RG behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02211",
  "author_total": 1,
  "authors": [
    {
      "name": "Ko Okumura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arf2zse21m0ga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02211",
  "fulltext_url": null,
  "id": "arf2zse21m0ga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02211",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7172392643",
  "pdf_url": "https://arxiv.org/pdf/2608.02211",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arf2zse21m0ga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2608.02211",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02211"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Renormalization-Group Stability Does Not Determine Front Selection",
  "title_text": "Renormalization-Group Stability Does Not Determine Front Selection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/arf2zse21m0ga",
  "venue": "arXiv",
  "versions": []
}