{
  "id": "1004.4873",
  "version": "v1",
  "published": "2010-04-27T17:53:02.000Z",
  "updated": "2010-04-27T17:53:02.000Z",
  "title": "Existence and Properties of Minimum Action Curves for Degenerate Finsler Metrics",
  "authors": [
    "Matthias Heymann"
  ],
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "I study a class of action functionals on the space of unparameterized oriented rectifiable curves in R^n. The local action is a degenerate type of Finsler metric that may vanish in certain directions, thus allowing for curves with positive Euclidean length but zero action. Given two sets A_1 and A_2, I develop criteria under which there exists a minimum action curve leading from A_1 to A_2. I then study the properties of these minimizers, and I prove the non-existence of minimizers in some situations. Applied to a geometric reformulation of the quasipotential of large deviation theory, my results can prove the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-27T17:53:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "51F99",
      "53C60"
    ],
    "keywords": [
      "minimum action curve",
      "degenerate finsler metrics",
      "properties",
      "maximum likelihood transition curves",
      "large deviation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4873H"
    }
  }
}