Loewner evolution driven by complex Brownian motion (with simulations by Minjae Park)

Ewain Gwynne, Joshua Pfeffer

We study the Loewner evolution whose driving function is $W_t=B_t^1+i{B}_t^2$, where $(B^1,B^2)$ is a pair of Brownian motions with a given covariance matrix. This model can be…