Existence of multi-point boundary Green's function for chordal Schramm-Loewner evolution (SLE)

2022/08/29 by Rami Fakhry, Fakhry, Rami, Dapeng Zhan +1
Mathematics · #60J67 #FOS: Mathematics #Meromorphic and Entire Functions #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2208.13667

openalex publication_date 2022/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we prove that, for κ∈(0,8), the n-point boundary Green's function of exponent \frac8κ-1 for chordal SLE_κ exists. We also prove that the convergence is uniform over compact sets and the Green's function is continuous. We also give up-to-constant bounds for the Green's function.

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