{
  "abstract": "A generalization of the exact overlaps conjecture predicts a formula for the dimension of self-similar measures in terms of the random walk entropy and the Lyapunov exponent. We prove the exact overlaps conjecture and its generalized version in dimension one. The proof relies on a new entropy inequality quantifying the information lost under addition of independent random variables in terms of a quantity averaging variance across scales.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10511",
  "author_total": 2,
  "authors": [
    {
      "name": "Samuel Kittle"
    },
    {
      "name": "Constantin Kogler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e58rgbgect50.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10511",
  "fulltext_url": null,
  "id": "1e58rgbgect50",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10511",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220980558",
  "pdf_url": "https://arxiv.org/pdf/2610.10511",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e58rgbgect50.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10511",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10511"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Exact Overlaps Conjecture for Self-Similar Measures on the Real Line",
  "title_text": "The Exact Overlaps Conjecture for Self-Similar Measures on the Real Line",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/1e58rgbgect50",
  "venue": "arXiv",
  "versions": []
}