{
  "id": "2103.10610",
  "version": "v1",
  "published": "2021-03-19T03:11:10.000Z",
  "updated": "2021-03-19T03:11:10.000Z",
  "title": "Speed of excited random walks with long backward steps",
  "authors": [
    "Tuan-Minh Nguyen"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a model of multi-excited random walk with non-nearest neighbour steps on $\\mathbb Z$, in which the walk can jump from a vertex $x$ to either $x+1$ or $x-i$ with $i\\in \\{1,2,\\dots,L\\}$, $L\\ge 1$. We first point out the multi-type branching structure of this random walk and then prove a limit theorem for a related multi-type Galton-Watson process with emigration, which is of independent interest. Combining this result and the method introduced by Basdevant and Singh [Probab. Theory Related Fields (2008), 141 (3-4)], we extend their result (w.r.t the case $L=1$) to our model. More specifically, we show that in the regime of transience to the right, the walk has positive speed if and only if the expected total drift $\\delta>2$. This confirms a special case of a conjecture proposed by Davis and Peterson.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-19T03:11:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J80",
      "60J85"
    ],
    "keywords": [
      "excited random walks",
      "long backward steps",
      "non-nearest neighbour steps",
      "related multi-type galton-watson process",
      "multi-excited random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}