= Boundary derivative diffusion under conformal Loewner conjugacy
{title2=$d a_t=\sqrt\kappa b_t\,dB_t+[b_t^2/(2a_t)+(\kappa/2-4/3)c_t]dt$}
Let $h_t$ intertwine two <Loewner chains>, with driver $\xi_t=\sqrt\kappa B_t$, and set $a_t=h_t'(\xi_t)$, $b_t=h_t''(\xi_t)$, $c_t=h_t'''(\xi_t)$. Expanding the conjugacy equation at the driver gives $\partial_t h_t'(\xi_t)=b_t^2/(2a_t)-4c_t/3$; the <Itô formula> gives the displayed diffusion. For a real exponent $p$, the drift of $a_t^p$ is $p[1+\kappa(p-1)]a_t^{p-2}b_t^2/2+p(\kappa/2-4/3)a_t^{p-1}c_t$. At $\kappa=8/3$, $p=5/8$ cancels both terms and yields the <SLE eight-thirds restriction martingale>.
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