{
  "id": "1601.02297",
  "version": "v1",
  "published": "2016-01-11T01:32:19.000Z",
  "updated": "2016-01-11T01:32:19.000Z",
  "title": "Eventual return probability in multidimensional random walks",
  "authors": [
    "Vyacheslav M. Abramov"
  ],
  "comment": "This is a new paper containing a principle and fundamental result in the theory of random walk",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "It is well-known that the simple symmetric random walk of dimension 1 or 2 is recurrent, i.e. being started from the origin, it returns to the original point infinitely many times. Simple symmetric random walks of dimension higher than 2 are not recurrent. The present paper derives simple limiting recurrence relations, which enable us to find an approximate value of the eventual return probability for a simple symmetric random walk of an arbitrary dimension $d$. The numerical calculations show that the eventual return probabilities for the simple symmetric random walks in ${Z}^3$ and ${Z}^4$ are close to 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-11T01:32:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J80",
      "60C05",
      "60K25"
    ],
    "keywords": [
      "eventual return probability",
      "simple symmetric random walk",
      "multidimensional random walks",
      "derives simple limiting recurrence",
      "simple limiting recurrence relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102297A"
    }
  }
}