{
  "id": "2312.08974",
  "version": "v1",
  "published": "2023-12-14T14:26:23.000Z",
  "updated": "2023-12-14T14:26:23.000Z",
  "title": "Multifractal analysis via Lagrange duality",
  "authors": [
    "Alex Rutar"
  ],
  "comment": "31 pages, 3 figures. This is an expository article. Comments, especially concerning presentation, are very welcome!",
  "categories": [
    "math.DS"
  ],
  "abstract": "We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the parametric geometry of the Lagrange dual associated with the constrained variational principle. We also give a direct derivation of the Hausdorff dimension of the level sets of the upper and lower local dimensions by exploiting certain weak uniformity properties of the space of Bernoulli measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-14T14:26:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "49N15",
      "94A17",
      "60F10"
    ],
    "keywords": [
      "multifractal analysis",
      "lagrange duality",
      "well-known multifractal formalism",
      "lower local dimensions",
      "strong separation condition"
    ],
    "tags": [
      "expository article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}