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

2023/09/09 by Lily Reeves, Reeves, Lily
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2309.04667

openalex publication_date 2023/09/09 · openalex created_date 2023/09/13 · openalex updated_date 2026/07/28

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 ≤ q ≤ 4. Along the way, we provide a complete proof of the strong arm separation lemma for the random cluster model.

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