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arXiv · 2309.04667

Nontrivial upper bound for chemical distance on the planar random cluster model

Lily Reeves
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Abstract

We extend the upper bounds derived for the horizontal and radial chemical distance for 2d Bernoulli percolation in [DHS21, SR20] to the planar random cluster model with cluster weight $1 \le q \le 4$. Along the way, we provide a complete proof of the strong arm separation lemma for the random cluster model.

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Lily Reeves. 2023-09-09. Nontrivial upper bound for chemical distance on the planar random cluster model. https://arxiv.org/abs/2309.04667

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