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Universality of Large-Scale Geometry For Critical Random-Cluster Models — arXiv:2611.00425

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00425
License (as archived): CC0-1.0
Archived: 2026-11-03T11:33:46.220Z
SHA-256 of the archived text: 36bfa8ed215486a769f41bb35fa1dd974a53c4cd26def306b321bcc7b6f2acd4
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How to cite

Universality of Large-Scale Geometry For Critical Random-Cluster Models — arXiv:2611.00425 — arXiv (en), https://arxiv.org/abs/2611.00425 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3be9db071284 (Metraipolis archive dc_3be9db071284, sha256 36bfa8ed215486a769f41bb35fa1dd974a53c4cd26def306b321bcc7b6f2acd4)

BibTeX

@misc{dc3be9db071284,
  title = {Universality of Large-Scale Geometry For Critical Random-Cluster Models — arXiv:2611.00425},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00425},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3be9db071284; sha256 36bfa8ed215486a769f41bb35fa1dd974a53c4cd26def306b321bcc7b6f2acd4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00425. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The understanding of the behaviour of critical lattice models in two dimensions has made immense progress in the past couple of decades, with conformal invariance as its conjectured end goal. We consider here the critical random-cluster model (or FK-percolation) on a large class of graphs --- namely bi-periodic isoradial graphs --- with cluster-weight~$q \in [1,4]$. Following up on the establishment of rotational invariance at criticality in \cite{Rotation}, we prove that the large scale behaviour of these models is asymptotically the same on all such graphs. These include the critical homogeneous models on the square, triangular and hexagonal lattices.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2611.00425 — 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 2026-11-03T11:04:52.211Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).