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Scaling limits for planar aggregation with subcritical fluctuations

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

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Scaling limits for planar aggregation with subcritical fluctuations. / Norris, James; Silvestri, Vittoria; Turner, Amanda.
In: Probability Theory and Related Fields, Vol. 185, No. 1-2, 28.02.2023, p. 185-250.

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

Harvard

Norris, J, Silvestri, V & Turner, A 2023, 'Scaling limits for planar aggregation with subcritical fluctuations', Probability Theory and Related Fields, vol. 185, no. 1-2, pp. 185-250. https://doi.org/10.1007/s00440-022-01141-0

APA

Norris, J., Silvestri, V., & Turner, A. (2023). Scaling limits for planar aggregation with subcritical fluctuations. Probability Theory and Related Fields, 185(1-2), 185-250. https://doi.org/10.1007/s00440-022-01141-0

Vancouver

Norris J, Silvestri V, Turner A. Scaling limits for planar aggregation with subcritical fluctuations. Probability Theory and Related Fields. 2023 Feb 28;185(1-2):185-250. Epub 2022 Jun 11. doi: 10.1007/s00440-022-01141-0

Author

Norris, James ; Silvestri, Vittoria ; Turner, Amanda. / Scaling limits for planar aggregation with subcritical fluctuations. In: Probability Theory and Related Fields. 2023 ; Vol. 185, No. 1-2. pp. 185-250.

Bibtex

@article{5362ad0c52ff42a88ce5818b00111360,
title = "Scaling limits for planar aggregation with subcritical fluctuations",
abstract = "We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.",
keywords = "math.PR, math-ph, math.CV, math.MP",
author = "James Norris and Vittoria Silvestri and Amanda Turner",
year = "2023",
month = feb,
day = "28",
doi = "10.1007/s00440-022-01141-0",
language = "English",
volume = "185",
pages = "185--250",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "1-2",

}

RIS

TY - JOUR

T1 - Scaling limits for planar aggregation with subcritical fluctuations

AU - Norris, James

AU - Silvestri, Vittoria

AU - Turner, Amanda

PY - 2023/2/28

Y1 - 2023/2/28

N2 - We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.

AB - We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.

KW - math.PR

KW - math-ph

KW - math.CV

KW - math.MP

U2 - 10.1007/s00440-022-01141-0

DO - 10.1007/s00440-022-01141-0

M3 - Journal article

VL - 185

SP - 185

EP - 250

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1-2

ER -