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Scaling limits for planar aggregation with subcritical fluctuations

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Scaling limits for planar aggregation with subcritical fluctuations. / Norris, James; Silvestri, Vittoria; Turner, Amanda.

In: arxiv.org, 04.02.2019.

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Norris, James ; Silvestri, Vittoria ; Turner, Amanda. / Scaling limits for planar aggregation with subcritical fluctuations. In: arxiv.org. 2019.

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@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 attachment point of each successive particle is distributed according to 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. ",
keywords = "math.PR, math-ph, math.CV, math.MP",
author = "James Norris and Vittoria Silvestri and Amanda Turner",
note = "51 pages, 7 figures",
year = "2019",
month = feb
day = "4",
language = "English",
journal = "arxiv.org",

}

RIS

TY - JOUR

T1 - Scaling limits for planar aggregation with subcritical fluctuations

AU - Norris, James

AU - Silvestri, Vittoria

AU - Turner, Amanda

N1 - 51 pages, 7 figures

PY - 2019/2/4

Y1 - 2019/2/4

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 attachment point of each successive particle is distributed according to 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.

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 attachment point of each successive particle is distributed according to 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.

KW - math.PR

KW - math-ph

KW - math.CV

KW - math.MP

M3 - Journal article

JO - arxiv.org

JF - arxiv.org

ER -