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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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One-dimensional scaling limits in a planar Laplacian random growth model. / Sola, Alan; Turner, Amanda; Viklund, Fredrik.
In: Communications in Mathematical Physics, Vol. 371, No. 1, 05.10.2019, p. 285-329.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Sola, A, Turner, A & Viklund, F 2019, 'One-dimensional scaling limits in a planar Laplacian random growth model', Communications in Mathematical Physics, vol. 371, no. 1, pp. 285-329. https://doi.org/10.1007/s00220-019-03460-1

APA

Sola, A., Turner, A., & Viklund, F. (2019). One-dimensional scaling limits in a planar Laplacian random growth model. Communications in Mathematical Physics, 371(1), 285-329. https://doi.org/10.1007/s00220-019-03460-1

Vancouver

Sola A, Turner A, Viklund F. One-dimensional scaling limits in a planar Laplacian random growth model. Communications in Mathematical Physics. 2019 Oct 5;371(1):285-329. Epub 2019 May 22. doi: 10.1007/s00220-019-03460-1

Author

Sola, Alan ; Turner, Amanda ; Viklund, Fredrik. / One-dimensional scaling limits in a planar Laplacian random growth model. In: Communications in Mathematical Physics. 2019 ; Vol. 371, No. 1. pp. 285-329.

Bibtex

@article{195c57f47dda424abb4140c33e969eea,
title = "One-dimensional scaling limits in a planar Laplacian random growth model",
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. ",
author = "Alan Sola and Amanda Turner and Fredrik Viklund",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-019-03460-1",
year = "2019",
month = oct,
day = "5",
doi = "10.1007/s00220-019-03460-1",
language = "English",
volume = "371",
pages = "285--329",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "1",

}

RIS

TY - JOUR

T1 - One-dimensional scaling limits in a planar Laplacian random growth model

AU - Sola, Alan

AU - Turner, Amanda

AU - Viklund, Fredrik

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-019-03460-1

PY - 2019/10/5

Y1 - 2019/10/5

N2 - 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.

AB - 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.

U2 - 10.1007/s00220-019-03460-1

DO - 10.1007/s00220-019-03460-1

M3 - Journal article

VL - 371

SP - 285

EP - 329

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -