Multipoint Estimates for Radial and Whole-plane SLE

2017/10/11 by Benjamin Mackey, Mackey, Benjamin, Dapeng Zhan +1
Mathematics · #30C #60G #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1710.04261

openalex publication_date 2017/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove upper bounds for the probability that a radial SLE_κ curve, κ∈(0,8), comes within specified radii of n different points in the unit disc. Using this estimate, we then prove a similar upper bound for a whole-plane SLE_κ curve. We then use these estimates to show that the lower Minkowski content of both the radial and whole-plane SLE_κ traces restricted in a bounded region have finite moments of any order.

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