{
  "id": "1212.1345",
  "version": "v4",
  "published": "2012-12-06T15:14:31.000Z",
  "updated": "2014-05-21T11:03:13.000Z",
  "title": "Exact dimensionality and projections of random self-similar measures and sets",
  "authors": [
    "Kenneth Falconer",
    "Xiong Jin"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact-dimensional, generalizing Feng and Hu's result \\cite{FeHu09} for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic self-similar measures \\cite{HoSh12} to these random measures without requiring any separation conditions on the underlying sets. We give applications to self-similar sets and fractal percolation, including new results on projections, $C^1$-images and distance sets.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-05-21T11:03:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random self-similar measures",
      "exact dimensionality",
      "projections",
      "multiplicative cascade measures",
      "self-similar sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.1345F"
    }
  }
}