{
  "id": "1703.09987",
  "version": "v1",
  "published": "2017-03-29T11:57:20.000Z",
  "updated": "2017-03-29T11:57:20.000Z",
  "title": "Dirichlet form associated with the $Φ_3^4$ model",
  "authors": [
    "Rongchan Zhu",
    "Xiangchan Zhu"
  ],
  "categories": [
    "math.PR",
    "math.AP",
    "math.FA"
  ],
  "abstract": "We construct the Dirichlet form associated with the dynamical $\\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient bilinear form is closable and then by a well-known result its closure is also a quasi-regular Dirichlet form, which means that there exists another (Markov) diffusion process, which also admits the $\\Phi^4_3$ field measure as an invariant (even symmetrizing) measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-29T11:57:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical gradient bilinear form",
      "quasi-regular dirichlet form",
      "cylinder functions",
      "well-known result",
      "diffusion process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}