Bond percolation on isoradial graphs: criticality and universality

@article{Grimmett2012BondPO,
  title={Bond percolation on isoradial graphs: criticality and universality},
  author={Geoffrey R. Grimmett and Ioan Manolescu},
  journal={Probability Theory and Related Fields},
  year={2012},
  volume={159},
  pages={273-327}
}
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the… 

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