{
  "abstract": "Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to ``Stochastic Localization,\" a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the $n$-dimensional Euclidean space - the domain of the probability distribution function appearing in the latter - is ``compactified'' to the surface of an $n$-dimensional sphere. By comparing the two frameworks, we argue that this compactification is a consequence of requiring the drift to be autonomous. The relationship between the two approaches may expand the scope of Stochastic Localization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36232",
  "author_total": 1,
  "authors": [
    {
      "name": "Ken Sekimoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fp5yvs06jbrad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36232",
  "fulltext_url": null,
  "id": "fp5yvs06jbrad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36232",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214910797",
  "pdf_url": "https://arxiv.org/pdf/2609.36232",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fp5yvs06jbrad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2609.36232",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36232"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Autonomous self-harmonic drift in Langevin dynamics causes a compaction of underlying domain for the density of Stochastic Localization",
  "title_text": "Autonomous self-harmonic drift in Langevin dynamics causes a compaction of underlying domain for the density of Stochastic Localization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/fp5yvs06jbrad",
  "venue": "arXiv",
  "versions": []
}