Skip to content
DraconiticResearch
Search Sources API
197,693 studies31 sourcesUpdated 38 min ago
PreprintCC BY 4.0arXiv

Universality of Large-Scale Geometry For Critical Random-Cluster Models

  • Ulrik Thinggaard Hansen
  • Ioan Manolescu
Open at sourcePDFDOICite

Abstract

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 ∈ [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.

Related

  1. Optimal detection of geometry in random graphs and kernel matrices at critical thresholds
    Cheng Mao, Timothy L. H. Wee
    arXivPreprintarXiv licenceFull textProbabilityStatisticsarXiv
  2. Edge universality of random regular graphs of growing degrees
    Jiaoyang Huang, Horng‐Tzer Yau
    The Annals of ProbabilityPeer-reviewedLicence not statedFull text16 citedStatisticsOpenAlex
  3. Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime
    Sofiia Dubova, Yue M. Lu, Benjamin McKenna +1
    The Annals of Applied ProbabilityPeer-reviewedLicence not statedFull text19 citedStatisticsOpenAlex
  4. Quantitative universality for products of i.i.d. random matrices
    Nikita Lvov
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices
    Ziyu Neroli
    arXivPreprintCC BY 4.0Full textMathematical physicsProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{hansen2026universality,
  title = {{Universality of Large-Scale Geometry For Critical Random-Cluster Models}},
  author = {Ulrik Thinggaard Hansen and Ioan Manolescu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00425},
  eprint = {2611.00425},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00425},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Universality of Large-Scale Geometry For Critical Random-Cluster Models
AU  - Ulrik Thinggaard Hansen
AU  - Ioan Manolescu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00425
UR  - https://arxiv.org/abs/2611.00425
AB  - 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 ∈ [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.
ER  -