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

Sola, Alan and Turner, Amanda and Viklund, Fredrik (2019) One-dimensional scaling limits in a planar Laplacian random growth model. Communications in Mathematical Physics, 371 (1). pp. 285-329. ISSN 0010-3616

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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.

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Journal Article
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Communications in Mathematical Physics
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24 Apr 2018 12:56
Last Modified:
22 Nov 2022 05:47