{
  "id": "1709.05092",
  "version": "v1",
  "published": "2017-09-15T08:08:22.000Z",
  "updated": "2017-09-15T08:08:22.000Z",
  "title": "Absolute continuity of non-homogeneous self-similar measures",
  "authors": [
    "Santiago Saglietti",
    "Pablo Shmerkin",
    "Boris Solomyak"
  ],
  "comment": "45 pages",
  "categories": [
    "math.DS",
    "math.CA",
    "math.PR"
  ],
  "abstract": "We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T08:08:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80",
      "37A45",
      "42A38"
    ],
    "keywords": [
      "non-homogeneous self-similar measures",
      "random self-similar measures",
      "real line",
      "understanding absolute continuity",
      "first improvement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}