The topology of SLE_κ is random for κ>4

2021/09/17 by Stephen Yearwood, Yearwood, Stephen
Mathematics · #60J67 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2109.08277

openalex publication_date 2021/09/17 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We study the topology of SLE curves for κ> 4. More precisely, we show that, a.s., there is no homeomorphism Φ: ℍ → ℍ, taking the range of one independent SLE curve to another for κ∈ (4,8). Furthermore, we extend the result to κ≥ 8 by showing that there is no homeomorphism taking one SLE curve to another, when viewed as curves modulo parametrization.

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