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Hastings-Levitov aggregation in the small-particle limit

Research output: Contribution to journalJournal article

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Hastings-Levitov aggregation in the small-particle limit. / Norris, James; Turner, Amanda.

In: Communications in Mathematical Physics, Vol. 316, No. 3, 12.2012, p. 809-841.

Research output: Contribution to journalJournal article

Harvard

Norris, J & Turner, A 2012, 'Hastings-Levitov aggregation in the small-particle limit', Communications in Mathematical Physics, vol. 316, no. 3, pp. 809-841. https://doi.org/10.1007/s00220-012-1552-6

APA

Norris, J., & Turner, A. (2012). Hastings-Levitov aggregation in the small-particle limit. Communications in Mathematical Physics, 316(3), 809-841. https://doi.org/10.1007/s00220-012-1552-6

Vancouver

Norris J, Turner A. Hastings-Levitov aggregation in the small-particle limit. Communications in Mathematical Physics. 2012 Dec;316(3):809-841. https://doi.org/10.1007/s00220-012-1552-6

Author

Norris, James ; Turner, Amanda. / Hastings-Levitov aggregation in the small-particle limit. In: Communications in Mathematical Physics. 2012 ; Vol. 316, No. 3. pp. 809-841.

Bibtex

@article{044e9472b2ca44089692cbba053243e9,
title = "Hastings-Levitov aggregation in the small-particle limit",
abstract = "We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Caratheodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web.",
author = "James Norris and Amanda Turner",
note = "The original publication is available at www.springerlink.com",
year = "2012",
month = dec
doi = "10.1007/s00220-012-1552-6",
language = "English",
volume = "316",
pages = "809--841",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",

}

RIS

TY - JOUR

T1 - Hastings-Levitov aggregation in the small-particle limit

AU - Norris, James

AU - Turner, Amanda

N1 - The original publication is available at www.springerlink.com

PY - 2012/12

Y1 - 2012/12

N2 - We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Caratheodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web.

AB - We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Caratheodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web.

U2 - 10.1007/s00220-012-1552-6

DO - 10.1007/s00220-012-1552-6

M3 - Journal article

VL - 316

SP - 809

EP - 841

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -