The random cluster model on the complete graph via large deviations

2022/01/14 by Darion Mayes, Mayes, Darion
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR

paper · pdf · doi:10.48550/arxiv.2201.05485

25 pages, no figures

openalex publication_date 2022/01/14 · arxiv created 2022/03/05 · arxiv updated 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the emergence of the giant component in the random cluster model on the complete graph, which was first studied by Bollobás, Grimmett, and Janson. We give an alternative analysis using a thermodynamic/large deviations approach introduced by Biskup, Chayes, and Smith for the case of percolation. In particular, we compute the rate function for large deviations of the size of the largest connected component of the random graph for q≥ 1.

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