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  • 1804.08462v1

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

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

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<mark>Journal publication date</mark>5/10/2019
<mark>Journal</mark>Communications in Mathematical Physics
Issue number1
Volume371
Pages (from-to)285-329
Publication statusPublished
Early online date22/05/19
Original languageEnglish

Abstract

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