{
  "abstract": "We study the one-dimensional stochastic Landau-Lifshitz-Gilbert equation with a regularised, multiplicative, degenerate trace-class noise of strength sqrt(eps), the regularisation being Q_delta^{1/2} = (I + delta A^{beta/2})^{-1}, A = -d^2/dx^2, beta > 3/2, and determine the exponential rate of thermally induced magnetisation reversal. (i) Uniform large deviations at fixed delta: for every delta > 0 the solution satisfies a large deviation principle on C([0,T];H), with a good rate function, uniformly in the initial datum over a V-bounded set with compact H-closure; no non-degeneracy of the noise is assumed. (ii) Removal of the regularisation: as delta tends to 0 the noise tends to space-time white noise. With U_delta the state-space quasi-potential and U_0 that of the limiting control problem (Q_0^{1/2} = I), U_delta converges to U_0 in the Gamma-sense, and the barrier is delta-independent: the infimum of U_delta over the boundary of D equals that of U_0 and equals c_* times the infimum of the micromagnetic energy E over that boundary, c_* = 2 lambda_2/(lambda_1^2 + lambda_2^2), under two structural assumptions only and with no geometric or transversality input. Pointwise convergence fails, so the Gamma-limit is the sharp form of the statement. (iii) Neel-Arrhenius law: combining (i) and (ii) with the classical exit-time theorem, the escape time tau from D = {E < r} satisfies both levels of the law - for every fixed delta > 0, eps log E[tau] converges, uniformly on compact subsets of the initial set, to the barrier, and lim_{delta->0} lim_{eps->0} eps log E[tau] = c_* times the infimum of E over the boundary of D. The Arrhenius exponent is therefore stable under the regularisation of the noise and is determined by the micromagnetic energy alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34823",
  "author_total": 3,
  "authors": [
    {
      "name": "Zdzisław Brzeźniak"
    },
    {
      "name": "Fan Gu"
    },
    {
      "name": "Liang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb0hmsnhsp9a7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34823",
  "fulltext_url": null,
  "id": "cb0hmsnhsp9a7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34823",
  "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",
      "math-ph"
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    [
      "arxiv",
      "math.AP"
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    [
      "arxiv",
      "math.MP"
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    [
      "arxiv",
      "math.PR"
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7224015309",
  "pdf_url": "https://arxiv.org/pdf/2610.34823",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb0hmsnhsp9a7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34823",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34823"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniform Large Deviations, Barrier Identity and the Néel--Arrhenius Law for the One-Dimensional Stochastic Landau--Lifshitz--Gilbert Equation",
  "title_text": "Uniform Large Deviations, Barrier Identity and the Néel--Arrhenius Law for the One-Dimensional Stochastic Landau--Lifshitz--Gilbert Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/cb0hmsnhsp9a7",
  "venue": "arXiv",
  "versions": []
}