{
  "id": "2301.05896",
  "version": "v1",
  "published": "2023-01-14T11:28:52.000Z",
  "updated": "2023-01-14T11:28:52.000Z",
  "title": "Geometric embedding for Regularity Structures",
  "authors": [
    "Yvain Bruned",
    "Foivos Katsetsiadis"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR",
    "math.AP",
    "math.RA"
  ],
  "abstract": "In this paper, we show how one can view certain models in Regularity Structures as some form of geometric rough paths. This is performed by identifying the deformed Butcher-Connes-Kreimer Hopf algebra with a quotient of the shuffle Hopf algebra which is the structure underlying the definition of a geometric rough path. This provides an extension of the isomorphism between the Butcher-Connes-Kreimer Hopf algebra and the shuffle Hopf algebra. This new algebraic result relies strongly on the deformation formalism and the post-Lie structures introduced recently in the context of Regularity Structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-14T11:28:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regularity structures",
      "shuffle hopf algebra",
      "geometric embedding",
      "geometric rough path",
      "deformed butcher-connes-kreimer hopf algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}