Remarks on the intersection of SLE_κ(ρ) curve with the real line

2015/07/01 by Menglu Wang, Hao Wu, Wang, Menglu +1
Engineering · Mathematics · #28A80 #60D05 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #math.PR #msc:28A80 #msc:60D05

paper · pdf · doi:10.48550/arxiv.1507.00218

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openalex publication_date 2015/07/01 · arxiv created 2015/10/09 · arxiv updated 2015/10/12 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

SLE_κ(ρ) is a variant of SLE_κ where ρ characterizes the repulsion (if ρ>0) or attraction (ρ<0) from the boundary. This paper examines the probabilities of SLE_κ(ρ) to get close to the boundary. We show how close the chordal SLE_κ(ρ) curves get to the boundary asymptotically, and provide an estimate for the probability that the SLE_κ(ρ) curve hits graph of functions. These generalize the similar result derived by Schramm and Zhou for standard SLE_κ curves.

Related

• Boundary proximity of SLE
• Duality of Chordal SLE, II
• Two-curve Green's function for 2-SLE: the interior case
• Ergodicity of the tip of an SLE curve
• Left Passage Probability of SLE(κ,ρ)