Green's function for cut points of chordal SLE attached with boundary arcs

2020/04/05 by Zhan, Dapeng
#60J67 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.02242

Abstract

Let κ∈(4,8). Let γ be an SLE_κ curve in a Jordan domain D connecting a₁≠ a₂∈∂ D. We attach γ with two open boundary arcs A₁,A₂ of D, which share end points b₁≠ b₂∈∂ D∖\a₁,a₂\, and consider for each z₀∈ D the limit lim_{r \downarrow 0}r^{1-\frac 38κ} ℙ[γ∪ A₁∪ A₂ has a cut point in \|z-z₀|

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• Two-curve Green's function for 2-SLE: the boundary case