{
  "id": "1306.3274",
  "version": "v2",
  "published": "2013-06-14T00:23:58.000Z",
  "updated": "2014-02-21T05:57:52.000Z",
  "title": "The exit time of planar Brownian motion and the Phragmen-Lindelof principle",
  "authors": [
    "Greg Markowsky"
  ],
  "categories": [
    "math.PR",
    "math.CV"
  ],
  "abstract": "In this note, we prove a version of the Phragmen-Lindelof principle using probabilistic techniques. In particular, we will show that if the p-th moment of the exit time of Brownian motion from a planar domain is finite, then an analytic function on that domain is either bounded by its supremum on the boundary or else goes to infinity along some sequence more rapidly than $e^{|z|^{2p}}$. We also present a method for constructing domains whose exit time has finite p-th moment, thereby giving a general Phragmen-Lindelof principle for spiral-like and star-like domains, and in the process giving a probabilistic proof of a theorem of Hansen. A number of auxiliary results are presented as well.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-21T05:57:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar brownian motion",
      "exit time",
      "finite p-th moment",
      "general phragmen-lindelof principle",
      "planar domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3274M"
    }
  }
}