Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-019-03460-1
Accepted author manuscript, 621 KB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Accepted author manuscript
Licence: None
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
<mark>Journal publication date</mark> | 5/10/2019 |
---|---|
<mark>Journal</mark> | Communications in Mathematical Physics |
Issue number | 1 |
Volume | 371 |
Pages (from-to) | 285-329 |
Publication Status | Published |
Early online date | 22/05/19 |
<mark>Original language</mark> | English |
We consider a family of growth models defined using conformal maps in which the local growth rate is determined by |Φn′|-η, where Φ 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 η> 1 , aggregating particles attach to their immediate predecessors with high probability, while for η< 1 almost surely this does not happen.