{
  "id": "1307.6830",
  "version": "v1",
  "published": "2013-07-25T18:13:51.000Z",
  "updated": "2013-07-25T18:13:51.000Z",
  "title": "Excursions of excited random walks on integers",
  "authors": [
    "Elena Kosygina",
    "Martin P. W. Zerner"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter delta. For recurrence/transience the critical threshold is |delta|=1, for ballisticity it is |delta|=2 and for diffusivity |delta|=4. In this paper we establish a phase transition at |delta|=3. We show that the expected return time of the walker to the starting point, conditioned on return, is finite iff |delta|>3. This result follows from an explicit description of the tail behaviour of the return time as a function of delta, which is achieved by diffusion approximation of related branching processes by squared Bessel processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-25T18:13:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60K37",
      "60F17",
      "60J70",
      "60J80",
      "60J85"
    ],
    "keywords": [
      "excited random walks",
      "excursions",
      "phase transition",
      "drift parameter delta",
      "expected return time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6830K"
    }
  }
}