Strict ordering threshold for SLE boundary swallowing (source code)

= Strict ordering threshold for SLE boundary swallowing
{title2=$\kappa\geq8$}

For $\kappa\geq8$, almost surely the positive-boundary swallowing times satisfy $T(x)<T(y)$ simultaneously for every $0<x<y$. The <SLE two-boundary-point ratio diffusion> has unbounded scale, ruling out escape before hitting $1$. For $4<\kappa<8$, its total scale $S_\kappa$ is finite, and the simultaneous-swallowing probability is $s_\kappa(y/(y-x))/S_\kappa$. At $\kappa=4$, fixed positive points have infinite swallowing times.