{
  "id": "2401.17243",
  "version": "v2",
  "published": "2024-01-30T18:37:01.000Z",
  "updated": "2025-05-08T00:57:47.000Z",
  "title": "Stochastic motions of the two-dimensional many-body delta-Bose gas, IV: Transformations of relative motions",
  "authors": [
    "Yu-Ting Chen"
  ],
  "comment": "Replacement of the paper with the same arXiv identifier by part of its second version, 8 pages. The other parts of the second version appear as arXiv:2505.01703, arXiv:2505.01704, and arXiv:2505.03006",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is the last in a series devoted to constructing stochastic motions representing the two-dimensional $N$-body delta-Bose gas for all integers $N\\geq 3$ via Feynman-Kac-type formulas. The main result here supplements [1,2] by proving a bijective transformation between two general classes of Langevin-type SDEs such that the solutions of the SDEs of one class recover precisely the stochastic relative motions associated with the solutions of the SDEs from the other class.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-08T00:57:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional many-body delta-bose gas",
      "transformation",
      "langevin-type sdes",
      "general classes",
      "stochastic relative motions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}