Critical percolation on mesoscopic triangulations

Vincent Beffara

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arXiv · 1312.7159

Critical percolation on mesoscopic triangulations

Vincent Beffara

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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.

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Vincent Beffara. 2013-12-26. Critical percolation on mesoscopic triangulations. https://arxiv.org/abs/1312.7159

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