{
  "abstract": "We establish an integration by parts formula for the semigroup in time $T>0$ of the kinetic Brownian motion in the Euclidean plane together with its velocity in the circle. The stochastic differential equation of our kinetic Brownian motion is driven here by one real-valued Brownian motion constructed from an orthonormal basis of $L^2([0,T],\\mathbb{R})$ and an independent sequence of $\\mathcal{N}(0,1)$ random variables. Our method is based on an explicit computation of a Malliavin dual in the Gaussian space. We are mainly interested in large time $T$. From our integration by parts, we obtain gradient estimates including a reverse Poincaré inequality for the semigroup. As a direct consequence, we also obtain a Liouville property for the generator of the kinetic Brownian motion and its speed: all bounded harmonic functions are constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Marc Arnaudon"
    },
    {
      "name": "Magalie Bénéfice"
    },
    {
      "name": "Michel Bonnefont"
    },
    {
      "name": "Delphine Féral"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cm37np93521ea.bib",
  "cited_by": 0,
  "doi": "10.3934/cpaa.2026100",
  "fulltext_url": null,
  "id": "cm37np93521ea",
  "issns": [
    "1534-0392",
    "1553-5258"
  ],
  "landing_url": "https://hal.science/hal-05556406v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
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    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7171982381",
  "pdf_url": "https://hal.science/hal-05556406/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-31",
  "publisher": "AIMS American Institute of Mathematical Sciences",
  "ris": "https://research.draconitic.com/paper/cm37np93521ea.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:35Z",
      "native_id": "hal-05556406",
      "source": "hal",
      "url": "https://hal.science/hal-05556406v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "Large time behaviour for the semigroup of the kinetic Brownian motion in the plane",
  "title_text": "Large time behaviour for the semigroup of the kinetic Brownian motion in the plane",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:35Z",
  "url": "https://research.draconitic.com/paper/cm37np93521ea",
  "venue": "Communications on Pure and Applied Analysis",
  "versions": []
}