  We consider multiple radial SLE as the number of curves tends to infinity. We
give conditions that imply the tightness of the associated processes given by
the Loewner equation. In the case of equal weights, the infinite-slit limit is
described by a Loewner equation whose Herglotz vector field is given by a
Burgers differential equation. Furthermore, we investigate a more general form
of the Burgers equation. On the one hand, it appears in connection with
semigroups of probability measures on the unit circle with respect to free
convolution. On the other hand, the Burgers equation itself is also a Loewner
differential equation for certain subordination chains.
