{
  "id": "2306.14849",
  "version": "v1",
  "published": "2023-06-26T17:00:16.000Z",
  "updated": "2023-06-26T17:00:16.000Z",
  "title": "On planar Brownian motion singularly tilted through a point potential",
  "authors": [
    "Jeremy Clark",
    "Barkat Mian"
  ],
  "comment": "75 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the two-dimensional Schr\\\"odinger operator with a point potential at the origin. These diffusions have a singular drift pointing in the direction of the origin that is strong enough to enable the possibly of visiting there, in contrast to a two-dimensional Brownian motion. Our main focus is on characterizing a local time process at the origin analogous to that for a one-dimensional Brownian motion and on studying the law of its process inverse.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-26T17:00:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G17",
      "60J55",
      "82C23",
      "82D60",
      "82B44"
    ],
    "keywords": [
      "planar brownian motion",
      "point potential",
      "one-dimensional brownian motion",
      "finite time interval",
      "transition density functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 75,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}