Critical percolation on mesoscopic triangulations
Probability
2014-10-03 v2
Abstract
We extend Smirnov's proof of the existence and conformal invariance of the scaling limit of critical site-percolation on the triangular lattice to particular sequences of periodic graphs with more arbitrary large-scale structure, obtained by piecing together triangular regions of the triangular lattice. While not formally speaking a scaling limit statement (as the graphs are not rescaled versions of each other), the result is a weak form of universality for critical percolation.
Cite
@article{arxiv.1312.7159,
title = {Critical percolation on mesoscopic triangulations},
author = {Vincent Beffara},
journal= {arXiv preprint arXiv:1312.7159},
year = {2014}
}