Two-sided SLE boundary swallowing probability
= Two-sided SLE boundary swallowing probability
{c}
For $1<d<2$, couple Bessel flows $X>0>Y$ with the same Brownian motion and let $v=x/y<0$. Then
$$
\mathbb P(\tau_x>\tau_y)=\frac{\displaystyle\int_v^0\frac{du}{(-u)^{d-1}(1-u)^{4-2d}}}{\displaystyle\int_{-\infty}^0\frac{du}{(-u)^{d-1}(1-u)^{4-2d}}}.
$$
It is the probability that the SLE hull swallows the chosen point on the negative side before the point on the positive side.