{
  "abstract": "For every $0<s<1$ we construct a compact $s$-Ahlfors regular set $K\\subset\\mathbb C$ for which harmonic measure of $\\mathbb C\\setminus K$ with pole at infinity is comparable to $\\mathcal H^s|_K$. In particular, there is no dimension drop for any dimension $s<1$. The construction is $N$-adic and based on configurations close to the $N$-th roots of unity. We adjust the positions of the children by small polynomial deformations so that the logarithmic potential of the natural Bernoulli measure becomes constant in the limit. A first-mode correction gives the range $s<2/3$, while corrections of arbitrary finite order yield the full range $0<s<1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15759",
  "author_total": 3,
  "authors": [
    {
      "name": "Yingying Cai"
    },
    {
      "name": "Cole Jeznach"
    },
    {
      "name": "Xavier Tolsa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p84ydtbh2ek6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15759",
  "fulltext_url": null,
  "id": "4p84ydtbh2ek6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15759",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221755083",
  "pdf_url": "https://arxiv.org/pdf/2610.15759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p84ydtbh2ek6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to $1$",
  "title_text": "Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to $1$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4p84ydtbh2ek6",
  "venue": "arXiv",
  "versions": []
}