{
  "abstract": "We establish quantitative hypocoercivity for singular stochastic damped wave equations arising in stochastic quantization. Building on the finite-dimensional argument of Cao, Lu, and Wang [Arch. Rat. Mech. Anal. 2023], we derive a dimension-free criterion that replaces uniform semiconvexity by a log-Sobolev inequality together with exponential lower-tail bounds for the bottom of the Hessian spectrum. We verify this criterion for the two-dimensional $Φ^4_2$ and sine-Gordon models and for the three-dimensional $Φ^4_3$ model, through estimates on the lowest eigenvalue of associated singular random Schrödinger operators. Combined with the continuum limit established in a companion paper, this yields exponential $L^2$ convergence to equilibrium for the $Φ^4_2$ dynamics and for sine-Gordon with $β^2<2π$. For $Φ^4_2$, we verify that in a weak-coupling, small-mass regime, optimizing the damping yields a kinetic relaxation rate of at least order $m$. This yields a genuine acceleration over the order-$m^2$ relaxation rate of the overdamped dynamics. The lattice estimates are uniform in the discretization for sine-Gordon throughout $β^2<4π$, and for $Φ^4_3$ at fixed volume, including regimes beyond those for which the continuum dynamics is vpresently constructed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17815",
  "author_total": 3,
  "authors": [
    {
      "name": "Nikolay Barashkov"
    },
    {
      "name": "Giacomo Di Gesù"
    },
    {
      "name": "Petri Laarne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f95svrr69g2qb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17815",
  "fulltext_url": null,
  "id": "f95svrr69g2qb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17815",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221835723",
  "pdf_url": "https://arxiv.org/pdf/2610.17815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f95svrr69g2qb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17815"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "$L^2$ convergence rates for singular stochastic wave dynamics",
  "title_text": "L^2 convergence rates for singular stochastic wave dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/f95svrr69g2qb",
  "venue": "arXiv",
  "versions": []
}