Existence and uniqueness of nonsimple multiple SLE

2023/08/26 by Dapeng Zhan, Zhan, Dapeng · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2308.13886

Abstract

We prove the existence and uniqueness of multiple SLE_κ associated with any given link pattern for κ∈ (4,6]. We also have the uniqueness for κ∈ (6,8). The multiple SLE_κ law is constructed by first inductively constructing a σ-finite multiple SLE_κ measure and then normalizing the measure whenever it is finite. The total mass of the measure satisfies the conformal covariance, asymptotics and PDE for multiple SLE_κ partition functions in the literature subject to the assumption that it is smooth.

Cited by

• Critical Ising model, Multiple SLE_κ((κ-6)/(2),(κ-6)/(2)) and β-Jacobi Ensemble

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