论文标题
Green的功能，用于与边界弧附着的弦SLE的切点
Green's function for cut points of chordal SLE attached with boundary arcs
论文作者
论文摘要
令$κ\ in（4,8）$。令$γ$为Jordan域中的SLE $_κ$曲线$ d $连接$ a_1 \ ne a_2 \ in \ partial d $。我们将$γ$带有两个开放边界弧$ a_1，a_2 $ $ d $，共享端点$ b_1 \ ne b_2 \ in \ in \ partial d \ setMinus \ {a_1，a_2 \} $，并考虑每个$ z_0 \ in d $ z_0 \ in d $ z_0 \ in d $ limud $ \ lim_ \ lim_ \ lim_ \ frof frow frow frow frow frow。 38κ} \ Mathbb {p} [γ\杯a_1 \ cup a_2 \ mbox {在} \ {| z-Z_0 | <r \}]中有一个切口。
Let $κ\in(4,8)$. Let $γ$ be an SLE$_κ$ curve in a Jordan domain $D$ connecting $a_1\ne a_2\in\partial D$. We attach $γ$ with two open boundary arcs $A_1,A_2$ of $D$, which share end points $b_1\ne b_2\in\partial D\setminus\{a_1,a_2\}$, and consider for each $z_0\in D$ the limit $$ \lim_{r \downarrow 0}r^{1-\frac 38κ} \mathbb{P}[γ\cup A_1\cup A_2 \mbox{ has a cut point in }\{|z-z_0|<r\}].$$ We prove that the limit converges, derive a rate of convergence, and obtain the exact formula of the limit up to a multiplicative constant depending only on $κ$.
