{
  "id": "2111.07381",
  "version": "v2",
  "published": "2021-11-14T16:12:59.000Z",
  "updated": "2023-11-11T21:47:28.000Z",
  "title": "The wave maps equation and Brownian paths",
  "authors": [
    "Bjoern Bringmann",
    "Jonas Luhrmann",
    "Gigliola Staffilani"
  ],
  "comment": "Minor changes to incorporate the reviewers' suggestions",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We discuss the $(1+1)$-dimensional wave maps equation with values in a compact Riemannian manifold $\\mathcal{M}$. Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold $\\mathcal{M}$ as initial data. Our main theorem is the probabilistic local well-posedness of the associated initial value problem. The analysis in this setting combines analytic, geometric, and probabilistic methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-11-11T21:47:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "53E99",
      "60L40"
    ],
    "keywords": [
      "brownian paths",
      "dimensional wave maps equation",
      "compact riemannian manifold",
      "gibbs measure problem",
      "probabilistic local well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}