{
  "abstract": "We establish a weighted Wasserstein spectral gap for the three-dimensional damped cubic wave equation with genuinely finite rank Brownian forcing. Under a saturation condition, the gap holds with respect to the negative phase topology $\\mathcal E_s=H^{-s}\\times H^{-1-s}$ for every $0<s<1/2$, from which we deduce unique ergodicity and exponential mixing in the energy topology. Sharp geometric characterizations of the saturation condition are also obtained. The method we develop is a stable--compact asymptotic coupling mechanism for hypoelliptic dissipative SPDEs beyond the parabolic setting. Instead of relying on positive time smoothing or asymptotic gradient estimates, it reduces the infinite-dimensional obstruction to contraction to a compact defect in a weaker coupling topology. Dense Malliavin range then permits this defect to be compensated by a finite dimensional Cameron--Martin shift, producing a finite distance contraction on bounded Lyapunov cores. Together with a separate high energy contraction from dissipation, this yields a global weighted Wasserstein spectral gap.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28459",
  "author_total": 2,
  "authors": [
    {
      "name": "Rongchang Liu"
    },
    {
      "name": "Kening Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10eegtm31pmk6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28459",
  "fulltext_url": null,
  "id": "10eegtm31pmk6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28459",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.28459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10eegtm31pmk6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28459"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Spectral gap for the three-dimensional damped cubic wave equation with degenerate noise",
  "title_text": "Spectral gap for the three-dimensional damped cubic wave equation with degenerate noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/10eegtm31pmk6",
  "venue": "arXiv",
  "versions": []
}