{
  "id": "2406.02988",
  "version": "v1",
  "published": "2024-06-05T06:38:10.000Z",
  "updated": "2024-06-05T06:38:10.000Z",
  "title": "Collapse of the Gibbs measure for the dynamical $Φ^3_2$-models on the infinite volume",
  "authors": [
    "Kihoon Seong",
    "Philippe Sosoe"
  ],
  "comment": "47 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We study the $\\Phi^3_2$-measure in the infinite volume limit. This is the invariant measure for several stochastic partial differential equations including the parabolic and hyperbolic $\\Phi^3_2$-models. In the large torus limit, we observe a concentration phenomenon of the $\\Phi^3_2$-measure around zero, which is the single minimizer of the corresponding Hamiltonian for any fixed torus size. From our sharp estimates for the partition function, we obtain a triviality result for the $\\Phi^3_2$-measure on infinite volume: the ensemble collapses onto a delta function on the zero field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T06:38:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gibbs measure",
      "stochastic partial differential equations",
      "infinite volume limit",
      "large torus limit",
      "delta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}