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The threshold for fractional clique decompositions of random hypergraphs, via matrix scaling — arXiv:2610.00924

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.00924
License (as archived): CC0-1.0
Archived: 2026-10-06T17:36:25.819Z
SHA-256 of the archived text: 609dcde25a56cde1529a9849293619077a46384b7cbbeed6839f28cb8944ac12
Stable URL of this page: https://metraipolis.com/documento/dc_f7ea441bbcb5

How to cite

The threshold for fractional clique decompositions of random hypergraphs, via matrix scaling — arXiv:2610.00924 — arXiv (en), https://arxiv.org/abs/2610.00924 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f7ea441bbcb5 (Metraipolis archive dc_f7ea441bbcb5, sha256 609dcde25a56cde1529a9849293619077a46384b7cbbeed6839f28cb8944ac12)

BibTeX

@misc{dcf7ea441bbcb5,
  title = {The threshold for fractional clique decompositions of random hypergraphs, via matrix scaling — arXiv:2610.00924},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.00924},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f7ea441bbcb5; sha256 609dcde25a56cde1529a9849293619077a46384b7cbbeed6839f28cb8944ac12},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.00924. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $\delta^*_{k,r}$ be the fractional $K_r^{(k)}$-decomposition threshold in minimum codegree. For fixed $k\ge2$, $r\ge k+1$ and $\varepsilon>0$, we prove that every $n$-vertex $k$-uniform hypergraph $G$ with minimum codegree at least $(\delta^*_{k,r}+\varepsilon)n$ admits, with high probability, a fractional $K_r^{(k)}$-decomposition after retaining each edge independently with probability $p \ge C(\log n/n^{r-k})^{1/(\binom{r}{k}-1)}$. The bound on $p$ is sharp up to a constant factor, confirming the conjectured threshold order in the graph case. The proof develops a probabilistic matrix-scaling approach.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.PR).
Categorie arXiv: Combinatorics (math.CO) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.00924 — 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 2026-10-06T16:02:27.504Z 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).