{
  "id": "2505.01703",
  "version": "v1",
  "published": "2025-05-03T05:51:16.000Z",
  "updated": "2025-05-03T05:51:16.000Z",
  "title": "Stochastic motions of the two-dimensional many-body delta-Bose gas, I: One-$δ$ motions",
  "authors": [
    "Yu-Ting Chen"
  ],
  "comment": "Part of the second version of arXiv:2401.17243, 57 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is the first in a series devoted to constructing stochastic motions for the two-dimensional $N$-body delta-Bose gas for all integers $N\\geq 3$ and establishing the associated Feynman-Kac-type formulas; see [11,12,13] for the remaining of the series. The main results of this paper establish the foundation by studying the stochastic one-$\\delta$ motions, which relate to the two-dimensional many-body delta-Bose gas by turning off all but one delta function, and we prove the central distributional properties and the SDEs. The proofs extend the method in [10] for the stochastic relative motions and develop and use analytical formulas of the probability distributions of the stochastic one-$\\delta$ motions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-03T05:51:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional many-body delta-bose gas",
      "central distributional properties",
      "stochastic relative motions",
      "constructing stochastic motions",
      "proofs extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}