{
  "id": "2408.13228",
  "version": "v1",
  "published": "2024-08-23T17:05:30.000Z",
  "updated": "2024-08-23T17:05:30.000Z",
  "title": "Quantitative weak mixing of self-affine tilings",
  "authors": [
    "Juan Marshall-Maldonado"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the regularity of spectral measures of dynamical systems arising from a translation action on tilings of substitutive nature. The results are inspired in the work of A. Bufetov and B. Solomyak, where they previously established a log-H\\\"older modulus of continuity of one-dimensional self-similar tiling systems. We generalize this result to higher dimension in the more general case of self-affine tilings systems. Futher analysis, leads to uniform estimates in the whole space of spectral parameters, allowing to deduce logarithmic rates of weak mixing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-23T17:05:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantitative weak mixing",
      "deduce logarithmic rates",
      "self-affine tilings systems",
      "one-dimensional self-similar tiling systems",
      "spectral parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}