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Exact Asymptotics for the Harmonic Descent Chain and Extended Convergence Bounds for Recursive Statistics — arXiv:2611.00347

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00347
License (as archived): CC0-1.0
Archived: 2026-11-03T18:46:39.465Z
SHA-256 of the archived text: 20f542b3b872c37107e2193d4f0448a8c09e974592668a8f545a60234db73d50
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How to cite

Exact Asymptotics for the Harmonic Descent Chain and Extended Convergence Bounds for Recursive Statistics — arXiv:2611.00347 — arXiv (en), https://arxiv.org/abs/2611.00347 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_320c28ced21a (Metraipolis archive dc_320c28ced21a, sha256 20f542b3b872c37107e2193d4f0448a8c09e974592668a8f545a60234db73d50)

BibTeX

@misc{dc320c28ced21a,
  title = {Exact Asymptotics for the Harmonic Descent Chain and Extended Convergence Bounds for Recursive Statistics — arXiv:2611.00347},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00347},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_320c28ced21a; sha256 20f542b3b872c37107e2193d4f0448a8c09e974592668a8f545a60234db73d50},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00347. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We give an exact asymptotic expansion of the occupation probabilities $a(n,k)$ of the harmonic descent chain, introduced by D. Aldous, as $n\rightarrow\infty$ with $k\in\mathrm{o}(\sqrt{n})$. In addition, we extend the recent results of Brandenberger et al. by giving a bound on the rate of convergence of sequences defined recursively by $x_n = \frac{1}{H_{n-1}}\sum_{i=1}^{n-1}\frac{x_i}{n-i}$ for more general initial conditions. This result enables the application of an existing central limit theorem, also by Brandenberger et al., to statistics of the critical beta-splitting tree which satisfy our more general initial conditions.

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/2611.00347 — 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 2026-11-03T18:15:07.685Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).