{
  "id": "1709.01253",
  "version": "v1",
  "published": "2017-09-05T06:35:27.000Z",
  "updated": "2017-09-05T06:35:27.000Z",
  "title": "Random walk on random walks: higher dimensions",
  "authors": [
    "Oriane Blondel",
    "Marcelo R. Hilario",
    "Renato Soares dos Santos",
    "Vladas Sidoravicius",
    "Augusto Teixeira"
  ],
  "comment": "38 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition kernels without the assumption of uniform ellipticity or nearest-neighbour jumps. Specifically, we obtain a strong law of large numbers, a functional central limit theorem and large deviation estimates for the position of the random walker under the annealed law in a high density regime. The main obstacle is the intrinsic lack of monotonicity in higher-dimensional, non-nearest neighbour settings. Here we develop more general renormalization and renewal schemes that allow us to overcome this issue. As a second application of our methods, we provide an alternative proof of the ballistic behaviour of the front of (the discrete-time version of) the infection model introduced in [23].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-05T06:35:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher dimensions",
      "dynamic random environment",
      "independent particles performing simple symmetric",
      "particles performing simple symmetric random",
      "functional central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}