{
  "id": "2505.03006",
  "version": "v1",
  "published": "2025-05-05T20:04:20.000Z",
  "updated": "2025-05-05T20:04:20.000Z",
  "title": "Stochastic motions of the two-dimensional many-body delta-Bose gas, III: Path integrals",
  "authors": [
    "Yu-Ting Chen"
  ],
  "comment": "Part of the second version of arXiv:2401.17243, 25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is the third 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. The main results here prove the Feynman-Kac-type formulas by using the stochastic many-$\\delta$ motions from [7] as the underlying diffusions. The associated multiplicative functionals show a new form and are derived from the analytic solutions of the two-dimensional $N$-body delta-Bose gas obtained in [4]. For completeness, the main theorem includes the formula for $N=2$, which is a minor modification of the Feynman--Kac-type formula proven in [5] for the relative motions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-05T20:04:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional many-body delta-bose gas",
      "stochastic motions",
      "path integrals",
      "feynman-kac-type formula proven",
      "main results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}