{
  "id": "2001.08330",
  "version": "v1",
  "published": "2020-01-23T01:29:31.000Z",
  "updated": "2020-01-23T01:29:31.000Z",
  "title": "Maximizing the $p$-th moment of exit time of planar Brownian motion from a given domain",
  "authors": [
    "Maher Boudabra",
    "Greg Markowsky"
  ],
  "categories": [
    "math.PR",
    "math.CV"
  ],
  "abstract": "In this paper we address the question of finding the point which maximizes the $p$-th moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method of excluding parts of the domain from consideration which makes use of a coupling argument and the conformal invariance of Brownian motion. In many cases the maximizing point can be localized to a relatively small region. Several illustrative examples are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-23T01:29:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar brownian motion",
      "exit time",
      "th moment",
      "maximizing",
      "conformal invariance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}