{
  "abstract": "Consider the diffusions $dX_t^\\varepsilon=b(X_t^\\varepsilon)dt+\\sqrt{2\\varepsilon}σ(X_t^\\varepsilon)dB_t$ on $\\mathbb{R}^d$, where $b$ and $σ$ are smooth coefficients and $B_t$ is an $r$-dimensional Brownian motion, with $r\\le d$. We allow nonreversible dynamics and a degenerate diffusion matrix. Let $\\mathcal{I}_\\varepsilon$ be the level-two large deviation rate functional of the empirical measure. Under our assumptions, including a complete metastable hierarchy described by resolvent convergence, we establish the full $Γ$-expansion $\\mathcal{I}_\\varepsilon=\\frac{1}{\\varepsilon}\\mathcal{J}^{(-1)}+\\mathcal{J}^{(0)}+\\sum_{p=1}^{\\mathfrak{q}}\\frac{1}{θ_\\varepsilon^{(p)}}\\mathcal{J}^{(p)}$ in the sense of successive $Γ$-limits in the weak topology on probability measures. Here $θ_\\varepsilon^{(p)}$ are the metastable time scales, and each $\\mathcal{J}^{(p)}$, $p\\ge1$, is the lift of the level-two rate functional of the corresponding finite-state Markov chain. We establish the pre-metastable $Γ$-limits for generalized overdamped, underdamped, and third-order Langevin dynamics. For the generalized overdamped model, existing metastability results yield the full expansion under additional conditions. For the underdamped and third-order models, the full expansion remains conditional on verification of the complete metastable hierarchy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22117",
  "author_total": 2,
  "authors": [
    {
      "name": "Donghyun Kim"
    },
    {
      "name": "Insuk Seo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xqhx4gnkpd35.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22117",
  "fulltext_url": null,
  "id": "2xqhx4gnkpd35",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22117",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222513636",
  "pdf_url": "https://arxiv.org/pdf/2610.22117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xqhx4gnkpd35.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Gamma Expansions of Level Two Large Deviation Rate Functionals for Metastable Diffusions",
  "title_text": "Gamma Expansions of Level Two Large Deviation Rate Functionals for Metastable Diffusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/2xqhx4gnkpd35",
  "venue": "arXiv",
  "versions": []
}