# Hyperbolic site percolation

@inproceedings{Grimmett2022HyperbolicSP, title={Hyperbolic site percolation}, author={Geoffrey R. Grimmett and Zhongyan Li}, year={2022} }

. Several results are presented for site percolation on quasi-transitive, planar graphs G with one end, when properly embedded in either the Euclidean or hyperbolic plane. If ( G 1 , G 2 ) is a matching pair derived from some quasi-transitive mosaic M , then p u ( G 1 ) + p c ( G 2 ) = 1, where p c is the critical probability for the existence of an inﬁnite cluster, and p u is the critical value for the existence of a unique such cluster. This fulﬁls and extends to the hyperbolic plane an…

## One Citation

### Percolation critical probabilities of matching lattice-pairs

- Mathematics
- 2022

. A necessary and suﬃcient condition is established for the strict inequality p c ( G ∗ ) < p c ( G ) between the critical probabilities of site percolation on a quasi-transitive, plane graph G and…

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