= SLE angle process
{c}
{title2=$\theta_t=\arg(g_t(z)-U_t)$}
With the upper-half-plane branch, $\theta_t\in(0,\pi)$ before the <Loewner swallowing time>. Write $Z_t=X_t+iY_t$. The <Itô formula> and the <Chordal Loewner equation> give
$$
d\theta_t=(\kappa-4)\frac{X_tY_t}{|Z_t|^4}\,dt+\sqrt\kappa\frac{Y_t}{|Z_t|^2}\,dB_t.
$$
At parameter four its drift vanishes. At other parameters the drift describes the competition between the deterministic conformal evolution and the Brownian driver.
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