Inhomogeneous bond percolation on square, triangular and hexagonal lattices

Geoffrey R. Grimmett; Ioan Manolescu

doi:10.1214/11-aop729

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arXiv · 1105.5535

Inhomogeneous bond percolation on square, triangular and hexagonal lattices

Geoffrey R. Grimmett·Ioan Manolescu

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Abstract

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. Among the consequences are box-crossing (RSW) inequalities for such models with parameter-values at which the transformation is valid. This is a step toward 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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BibTeX RIS

Geoffrey R. Grimmett, Ioan Manolescu. 2011-05-27. Inhomogeneous bond percolation on square, triangular and hexagonal lattices. https://doi.org/10.1214/11-aop729

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