{
  "id": "2107.10775",
  "version": "v1",
  "published": "2021-07-22T16:03:46.000Z",
  "updated": "2021-07-22T16:03:46.000Z",
  "title": "Dyson's model in infinite dimensions is irreducible",
  "authors": [
    "Hirofumi Osada",
    "Ryosuke Tsuboi"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Dyson's model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of $ \\beta = 2$. The stochastic process is given as a solution to an infinite-dimensional stochastic differential equation. Additionally, a Dirichlet form with the sine$ _2$ point process as a reference measure constructs the stochastic process as a functional of the associated configuration-valued diffusion process. In this paper, we prove that Dyson's model in infinite dimensions is irreducible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-22T16:03:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60H10",
      "60J40",
      "60J60",
      "60K35"
    ],
    "keywords": [
      "infinite dimensions",
      "dysons model",
      "infinite-dimensional stochastic differential equation",
      "stochastic process",
      "irreducible"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}