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Permutations from ranking independent random variables — arXiv:2610.11895

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.11895
License (as archived): CC0-1.0
Archived: 2026-10-09T06:28:25.743Z
SHA-256 of the archived text: 7ba25427eaaa95233fbd714dd2829d0bcc53d2b87ce2138e45130ee037243483
Stable URL of this page: https://metraipolis.com/documento/dc_3587ff9537cc

How to cite

Permutations from ranking independent random variables — arXiv:2610.11895 — arXiv (en), https://arxiv.org/abs/2610.11895 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3587ff9537cc (Metraipolis archive dc_3587ff9537cc, sha256 7ba25427eaaa95233fbd714dd2829d0bcc53d2b87ce2138e45130ee037243483)

BibTeX

@misc{dc3587ff9537cc,
  title = {Permutations from ranking independent random variables — arXiv:2610.11895},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.11895},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3587ff9537cc; sha256 7ba25427eaaa95233fbd714dd2829d0bcc53d2b87ce2138e45130ee037243483},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.11895. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $X_1,\ldots,X_n$ be almost surely distinct independent real-valued random variables. Let $\sigma$ be the random permutation of $\{1,\ldots,n\}$ such that $X_{\sigma(1)}<X_{\sigma(2)}<\cdots< X_{\sigma(n)}$. We show that the set of laws of $\sigma$, as the laws of $X_1,\ldots,X_n$ vary, has semialgebraic dimension \[ \sum_{k=2}^n {n \choose k}(k-1)! \] as a subset of the $(n!-1)$-simplex. This establishes a conjecture of Babson, Duchin, Iseli, Poggi-Corradini, Thurston, and Tucker-Foltz who proved that the dimension is upper bounded by the above expression. We prove their conjecture by constructing a family of finitely supported laws for $X_1,\ldots,X_n$ that provides the correct dimension. We also give an alternative proof of the upper bound using a theorem of Radford. Furthermore, we show that the Mallows law on permutations cannot arise as a law of $\sigma$ for $n\geq 4$, answering a question of Ed Crane.

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/2610.11895 — 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 2026-10-09T05:53:01.696Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).