{
  "abstract": "We study an accelerated Langevin equation in which the classical overdamped Langevin drift is supplemented by a nonlocal gradient velocity determined through a target-weighted Poisson equation. The target $p$ is only assumed to be strictly positive and need not be normalized. Writing the dynamics in terms of $ω=\\log(p/q)$ yields a coupled parabolic-elliptic system whose parabolic component contains the usual Langevin diffusion, whereas the elliptic component generates a global transport. The system is invariant under multiplication of $p$ by a positive constant. On a bounded smooth domain with homogeneous Neumann boundary conditions, we establish global existence and uniqueness of classical solutions for strictly positive $C^{2+α}$ target weights and compatible $C^{2+α}$ initial data. For long-time behavior, the oscillation of $ω$ decays at the explicit rate $e^{-t}$ and the solution density exponentially converges to target density. Moreover, an exact entropy-dissipation identity holds relative to the target density, in which the relative Fisher information and the Jeffreys divergence give the two dissipation mechanisms associated with the Langevin and weighted-Poisson components. In particular, KL divergence also converges to zero with rate $e^{-t}$ without a convexity assumption on the target.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35892",
  "author_total": 4,
  "authors": [
    {
      "name": "Ziyue Cai"
    },
    {
      "name": "Weiye Gan"
    },
    {
      "name": "Borui Miao"
    },
    {
      "name": "Zuoqiang Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yn722hxxchym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35892",
  "fulltext_url": null,
  "id": "9yn722hxxchym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35892",
  "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"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7224092672",
  "pdf_url": "https://arxiv.org/pdf/2610.35892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yn722hxxchym.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Accelerating Langevin Dynamics with Weighted Laplacian Flow: Global Well-Posedness and Exponential Convergence",
  "title_text": "Accelerating Langevin Dynamics with Weighted Laplacian Flow: Global Well-Posedness and Exponential Convergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/9yn722hxxchym",
  "venue": "arXiv",
  "versions": []
}