{
  "abstract": "We study stochastic fast-slow systems with noise acting exclusively on the slow variable near uniformly attracting, normally hyperbolic critical manifolds $x=X^\\ast(y)$. The deviation equation contains transmitted diffusion and an Itô curvature forcing of order $O(σ^2\\lVert D^2X^\\ast\\rVert)$. Using a parameter-dependent Lyapunov function and stopped martingale estimates, we obtain geometry-dependent concentration bounds under the sufficient noise restriction $σ\\le C_0\\min(\\sqrt{\\varepsilon},\\varepsilon^{1/4}L_{\\mathrm{geom}}/\\sqrt{λ_0})$, where $λ_0$ is the uniform spectral gap and $L_{\\mathrm{geom}}=\\sqrt{λ_0/(\\lVert D^2X^\\ast\\rVert\\lVert h\\rVert^2)}$. For fixed geometry and any fixed $p>0$, the confidence radius on $[0,T/\\varepsilon]$ is $O(\\varepsilon+σ^2+σ\\sqrt{\\log(1/\\varepsilon)})$, with stopped fast-variable failure probability at most $\\varepsilon^p$; slow-variable exit is controlled separately. We also establish an adiabatic error bound of order $O(\\varepsilon+σ\\sqrt{\\varepsilon}+σ^2\\lVert D^2X^\\ast\\rVert)$, with explicit failure probabilities. These estimates quantify the curvature dependence of fast-variable concentration and its $O(\\varepsilon)$ contribution to the slow-error upper bound for fixed geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16217",
  "author_total": 1,
  "authors": [
    {
      "name": "Yefan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ggg9cby6nm11.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16217",
  "fulltext_url": null,
  "id": "3ggg9cby6nm11",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16217",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2612|Differential Equations and Numerical Methods"
    ]
  ],
  "openalex": "W7169868388",
  "pdf_url": "https://arxiv.org/pdf/2607.16217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ggg9cby6nm11.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2607.16217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16217"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Curvature-Dependent Path Concentration in Stochastic Fast-Slow Systems with Noise on the Slow Variable",
  "title_text": "Curvature-Dependent Path Concentration in Stochastic Fast-Slow Systems with Noise on the Slow Variable",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/3ggg9cby6nm11",
  "venue": "arXiv",
  "versions": []
}