{
  "id": "1410.4814",
  "version": "v1",
  "published": "2014-10-17T18:21:41.000Z",
  "updated": "2014-10-17T18:21:41.000Z",
  "title": "Conditioned, quasi-stationary, restricted measures and escape from metastable states",
  "authors": [
    "Roberto Fernandez",
    "Francesco Manzo",
    "Francesca Nardi",
    "Elisabetta Scoppola",
    "Julien Sohier"
  ],
  "comment": "39 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic hitting time $\\tau^{(n)}$ of a family of Markov processes $X^{(n)}$ to a target set $G^{(n)}$ when the process starts from a trap defined by very general properties. We give an explicit description of the law of $X^{(n)}$ conditioned to stay within the trap, and from this we deduce the exponential distribution of $\\tau^{(n)}$. Our approach is very broad ---it does not require reversibility, the target $G$ does not need to be a rare event, and the traps and the limit on $n$ can be of very general nature--- and leads to explicit bounds on the deviations of $\\tau^{(n)}$ from exponentially. We provide two non trivial examples to which our techniques directly apply.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-17T18:21:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60J28",
      "82C05"
    ],
    "keywords": [
      "restricted measures",
      "metastable states",
      "quasi-stationary",
      "non trivial examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4814F"
    }
  }
}