Home > Research > Publications & Outputs > One-dimensional scaling limits in a planar Lapl...

### Electronic data

• 1804.08462v1

Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-019-03460-1

Accepted author manuscript, 620 KB, PDF-document

## One-dimensional scaling limits in a planar Laplacian random growth model

Research output: Contribution to journalJournal article

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 form of straight slits. More precisely, we exhibit a phase transition in the ancestral structure of the growing clusters: for $\eta>1$, aggregating particles attach to their immediate predecessors with high probability, while for \$\eta