Boundary-point Bessel flow for SLE

For chordal ${\mathrm{SLE}}_{\kappa }$, the centered image of a real boundary point, divided by $\sqrt{\kappa }$, evolves as a Bessel process of dimensionIts first hit of zero is the time at which the point is swallowed by the Loewner hull.

For $1<d<2$, couple Bessel flows $X>0>Y$ with the same Brownian motion and let $v=x/y<0$. ThenIt is the probability that the SLE hull swallows the chosen point on the negative side before the point on the positive side.