Percolation on dual lattices with k-fold symmetry
| dc.creator | Bollobas, Bela | |
| dc.creator | Riordan, Oliver | |
| dc.date | 2006-06-07 | |
| dc.date | 2007-02-06 | |
| dc.date.accessioned | 2026-07-07T13:12:46Z | |
| dc.date.available | 2026-07-07T13:12:46Z | |
| dc.description | Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an infinite open cluster when it exists; this argument requires some symmetry. Here we show that a simple modification of Zhang's argument requires only 2-fold (or 3-fold) symmetry, proving that the critical probabilities for percolation on dual planar lattices with such symmetry sum to 1. Like Zhang's argument, our extension applies in many contexts; in particular, it enables us to answer a question of Grimmett concerning the anisotropic random cluster model on the triangular lattice. | |
| dc.description | 11 pages, 1 figure. Revised with applications added; to appear in Random Structures and Algorithms | |
| dc.identifier | https://arxiv.org/abs/math/0606149 | |
| dc.identifier | http://arxiv.org/abs/math/0606149 | |
| dc.identifier | Random Structures and Algorithms 32 (2008), 463--472. | |
| dc.identifier | doi:10.1002/rsa.20205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229674 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60K35; 82B43 | |
| dc.title | Percolation on dual lattices with k-fold symmetry | |
| dc.type | text |