One-Dimensional Scaling Limits in a Planar Laplacian Random Growth Model
One-Dimensional Scaling Limits in a Planar Laplacian Random Growth Model
We consider a family of growth models defined using conformal maps in which the local growth rate is determined by $|\Phi_n'|^{-\eta}$, where $\Phi_n$ is the aggregate map for $n$ particles. We establish a scaling limit result in which strong feedback in the growth rule leads to one-dimensional limits in the …