Equivalence of Polychromatic Arm Probabilities on the Square Lattice
Probability
2022-01-31 v2
Abstract
We consider 2d critical Bernoulli percolation on the square lattice. We prove an approximate color-switching lemma comparing k-arm probabilities for different polychromatic color sequences. This result is well-known for site percolation on the triangular lattice in [Nolin08]. To handle the complications arising from the dual lattice, we introduce a shifting transformation to convert arms between the primal and dual lattices.
Keywords
Cite
@article{arxiv.2009.07029,
title = {Equivalence of Polychromatic Arm Probabilities on the Square Lattice},
author = {Lily Reeves and Philippe Sosoe},
journal= {arXiv preprint arXiv:2009.07029},
year = {2022}
}
Comments
Revision of an auxiliary lemma and other text edits. arXiv admin note: text overlap with arXiv:2001.07872