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Chaining, tree and measure for some canonical processes — arXiv:2610.01709

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01709
License (as archived): CC0-1.0
Archived: 2026-10-06T17:36:31.290Z
SHA-256 of the archived text: 7f5d80ce921c7eddaa50d8f3127b47a11c1c1b3d35d170060a82193676276e42
Stable URL of this page: https://metraipolis.com/documento/dc_bb83f52e560d

How to cite

Chaining, tree and measure for some canonical processes — arXiv:2610.01709 — arXiv (en), https://arxiv.org/abs/2610.01709 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bb83f52e560d (Metraipolis archive dc_bb83f52e560d, sha256 7f5d80ce921c7eddaa50d8f3127b47a11c1c1b3d35d170060a82193676276e42)

BibTeX

@misc{dcbb83f52e560d,
  title = {Chaining, tree and measure for some canonical processes — arXiv:2610.01709},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01709},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bb83f52e560d; sha256 7f5d80ce921c7eddaa50d8f3127b47a11c1c1b3d35d170060a82193676276e42},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01709. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove two deterministic results for families of distances arising in the study of canonical processes. The first derives an admissible partition scheme from a growth condition. The second gives a representation in terms of parameterized separation trees and compares it with the corresponding majorizing-measure quantities. The main point is that the proofs do not depend on the distribution of the underlying process: once the initial distance and the family of distances are given, no random variables, independence, tail functions, or moment estimates are used. For canonical processes with regular log-concave tails, the assumptions of the abstract results follow from the usual regularity conditions. One direction of the separation-tree estimate also applies to Bernoulli processes without these additional assumptions, and we prove the reverse estimate for bounded convex unconditional index sets. We also give a version of the growth argument for points which, for finite index sets, leads to a recursive construction of admissible partitions and parameterized separation trees.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.PR).
Categorie arXiv: Functional Analysis (math.FA) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.01709 — 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 2026-10-06T16:02:27.509Z dalla pagina https://arxiv.org/catchup/math.PR/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).