Brownian entrance law to a disc from infinity
= Brownian entrance law to a disc from infinity
For planar Brownian motion started at $iy$, the distribution of its first hit of the closed unit disc converges as $y\to\infty$ to normalized arc length on the unit circle. Inversion maps the exterior disc to the punctured disc and the starting point to $-i/y\to0$, where rotational invariance makes harmonic measure uniform.