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In the half-plane-capacity parameterization, let $W$ be standard real Brownian motion and put ${\xi }_t=\sqrt{\kappa }{W}_t$. Solve the Chordal Loewner equationThe points for which this flow ceases to exist form the growing compact H-hulls $K_t$, with half-plane capacity $2t$. The process is an SLE trace when its initial segments generate these hulls andThe limit is the continuous trace of a Loewner chain started at zero. If the curve disconnects a region from infinity, that region is included in $K_t$; the hull is not generally just the visited curve. For $\kappa =0$ the driver is identically zero and the trace is the deterministic vertical slit ${\gamma }_t=2i\sqrt{t}$.

Use the following deterministic boundary fact from the Chordal Loewner equation. For a continuous trace of a Loewner chain started at zero and generating its hulls, the real flow at $b>0$ has a boundary swallowing time $T_b$. Until that time it is the reflected boundary value of $g_t$, andA finite $T_b$ is its first collision with the driver, $X_t\to 0$ as $t\uparrow T_b$. Topologically, the boundary point $b$ is then visited or separated from infinity precisely when the trace has reached some point in $[b,\infty )$. A boundary crosscut can swallow an interval, so this is not a claim that the trace visits the particular point $b$.

Consequently the SLE boundary swallowing criterion isFor the SLE driver this real flow obeysup to its first hit of zero. This is the Boundary-point Bessel flow for SLE.