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Uniform Dimension Theorem for SLE in Natural Time — arXiv:2611.02493

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02493
License (as archived): CC0-1.0
Archived: 2026-11-03T11:34:36.173Z
SHA-256 of the archived text: 61c89dcf31317b42d24718b343d85b028f7afb40780476ff05ed55c980c69af3
Stable URL of this page: https://metraipolis.com/documento/dc_705fe5be5886

How to cite

Uniform Dimension Theorem for SLE in Natural Time — arXiv:2611.02493 — arXiv (en), https://arxiv.org/abs/2611.02493 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_705fe5be5886 (Metraipolis archive dc_705fe5be5886, sha256 61c89dcf31317b42d24718b343d85b028f7afb40780476ff05ed55c980c69af3)

BibTeX

@misc{dc705fe5be5886,
  title = {Uniform Dimension Theorem for SLE in Natural Time — arXiv:2611.02493},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02493},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_705fe5be5886; sha256 61c89dcf31317b42d24718b343d85b028f7afb40780476ff05ed55c980c69af3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02493. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For $0<\kappa<8$, we prove a uniform dimension transformation theorem for SLE in natural time: on a single probability-one event, Hausdorff and packing dimensions of every time set are multiplied by $d=1+\kappa/8$, and the same holds for lower and upper box dimensions of every bounded time set. The result applies to self-similar SLE with stationary increments, chordal SLE in the half-plane, and chordal SLE in bounded piecewise $C^1$ Jordan domains. In the last case, the box-dimension conclusion holds under a positive-angle endpoint hypothesis. We also establish boundary-inclusive local Hölder continuity of every order below $1/d$ for chordal SLE in natural time and identify the exact local dimension $d$ of the natural occupation measure on compact time intervals.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2611.02493 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:04:52.268Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).