{
  "id": "1610.06123",
  "version": "v1",
  "published": "2016-10-19T17:41:03.000Z",
  "updated": "2016-10-19T17:41:03.000Z",
  "title": "Decay of correlations and laws of rare events for random maps with a dense orbit",
  "authors": [
    "Vitor Araujo",
    "Hale Aytaç"
  ],
  "comment": "1 figure; 20 pages. arXiv admin note: text overlap with arXiv:1605.07006 by other authors",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We show that uniformly continuous random perturbations of maps with a dense orbit define an aperiodic Harris chain which also satisfies Doeblin's condition. As a result, we get exponential decay of correlations for suitable random perturbations of such systems. We also prove that, for maps with a forward dense orbit, the limiting distribution for Extreme Value Laws (EVLs) and Hitting/Return Time Statistics (HTS/RTS) is standard exponential. Moreover, we show that the Rare Event Point Process (REPP) converges in distribution to a standard Poisson process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-19T17:41:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A50",
      "60G70",
      "37B20",
      "60G10",
      "37A25",
      "37H99"
    ],
    "keywords": [
      "random maps",
      "correlations",
      "rare event point process",
      "extreme value laws",
      "satisfies doeblins condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}