Conformal invariance of planar Brownian motion
= Conformal invariance of planar Brownian motion
If $B$ is planar <Brownian motion> in a domain $D$ and $f:D\to D'$ is a nonconstant <holomorphic function>, then $f(B)$, run with the clock $\int_0^t|f'(B_s)|^2ds$, is planar Brownian motion in $D'$ until the relevant exit time. In particular, <conformal maps> transport <harmonic measure> between planar domains.