Inhomogeneous bond percolation on square, triangular, and hexagonal lattices

Details Inhomogeneous bond percolation on square, triangular, and hexagonal lattices Inhomogeneous bond percolation on square, triangular, and hexagonal lattices

2011-05-27

arxiv.org/abs/1105.5535v2

Mathematics

Probability

Minor changes for v2. To appear in The Annals of Probability

Scientific paper

The star-triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices. Amongst the consequences are box-crossing (RSW) inequalities for such models with parameter-values at which the transformation is valid. This is a step towards proving the universality and conformality of these processes. It implies criticality of such values, thereby providing a new proof of the critical point of inhomogeneous systems. The proofs extend to certain isoradial models to which previous methods do not apply.

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