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

Lily Reeves

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

Probability 2023-09-12 v1

Authors: Lily Reeves

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.

Keywords

random cluster model chemical distance bernoulli percolation upper bound strong arm separation lemma

Cite

@article{arxiv.2309.04667,
  title  = {Nontrivial upper bound for chemical distance on the planar random cluster model},
  author = {Lily Reeves},
  journal= {arXiv preprint arXiv:2309.04667},
  year   = {2023}
}

Comments

27 pages, 4 figures, comments welcome

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