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Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution — arXiv:2609.29882

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.29882
License (as archived): CC0-1.0
Archived: 2026-10-08T06:08:11.293Z
SHA-256 of the archived text: 51ccff6a1571752cefb917f7b237e7b5ac8de728be114a906d18ee31d519ffa0
Stable URL of this page: https://metraipolis.com/documento/dc_52a67e136b34

How to cite

Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution — arXiv:2609.29882 — arXiv (en), https://arxiv.org/abs/2609.29882 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_52a67e136b34 (Metraipolis archive dc_52a67e136b34, sha256 51ccff6a1571752cefb917f7b237e7b5ac8de728be114a906d18ee31d519ffa0)

BibTeX

@misc{dc52a67e136b34,
  title = {Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution — arXiv:2609.29882},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.29882},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_52a67e136b34; sha256 51ccff6a1571752cefb917f7b237e7b5ac8de728be114a906d18ee31d519ffa0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.29882. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We identify the optimal constant and describe all maximizers for the Fourier endpoint extension inequality associated with the moment curve over finite fields. This confirms a conjecture proposed in the authors' earlier work. The proof proceeds by showing that the problem is equivalent to a purely probabilistic extremal statement: among all probability distributions on a finite set, the uniform distribution uniquely maximizes the expected number of distinct rearrangements of an i.i.d. sample.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.PR).
Categorie arXiv: Classical Analysis and ODEs (math.CA) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.29882 — 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 2026-10-08T05:35:05.180Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).