Multiple SLE_κ from CLE_κ for κ∈ (4,8)

2025/03/11 by Valeria Ambrosio, Ambrosio, Valeria, Jason Miller +3
Mathematics · #30C20 (Secondary) #60J67 (Primary) 60K35 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2503.08958

openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define multichordal CLE_κ for κ∈ (4,8) as the conditional law of the remainder of a partially explored CLE_κ. The strands of a multichordal CLE_κ have a random link pattern, and their law conditionally on the linking pattern is a (global) multichordal SLE_κ. The multichordal CLE_κ are the conjectural scaling limits of FK and loop O(n) models with some wiring patterns of the boundary arcs. We also explain how CLE_κ configurations can be locally resampled, and show that the partially explored strands can be relinked in any possible way with positive probability. We will also establish several other estimates for partially explored CLE_κ. Altogether, these relationships and results serve to provide a toolbox for studying CLE_κ and global multiple SLE_κ.

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