Inhomogeneous bond percolation on square, triangular and hexagonal lattices
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.
Cite
@article{arxiv.1105.5535,
title = {Inhomogeneous bond percolation on square, triangular and hexagonal lattices},
author = {Geoffrey R. Grimmett and Ioan Manolescu},
journal= {arXiv preprint arXiv:1105.5535},
year = {2021}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AOP729 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)