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Scaling limits and fluctuations for random growth under capacity rescaling

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Scaling limits and fluctuations for random growth under capacity rescaling. / Liddle, George; Turner, Amanda.
In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Vol. 57, No. 2, 31.05.2021, p. 980-1015.

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

Harvard

Liddle, G & Turner, A 2021, 'Scaling limits and fluctuations for random growth under capacity rescaling', Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, vol. 57, no. 2, pp. 980-1015. https://doi.org/10.1214/20-AIHP1104

APA

Liddle, G., & Turner, A. (2021). Scaling limits and fluctuations for random growth under capacity rescaling. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 57(2), 980-1015. https://doi.org/10.1214/20-AIHP1104

Vancouver

Liddle G, Turner A. Scaling limits and fluctuations for random growth under capacity rescaling. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2021 May 31;57(2):980-1015. doi: 10.1214/20-AIHP1104

Author

Liddle, George ; Turner, Amanda. / Scaling limits and fluctuations for random growth under capacity rescaling. In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2021 ; Vol. 57, No. 2. pp. 980-1015.

Bibtex

@article{60a04352bf8a45f284b19cb19a04ea08,
title = "Scaling limits and fluctuations for random growth under capacity rescaling",
abstract = "We evaluate a strongly regularised version of the Hastings-Levitov model HL$(\alpha)$ for $0\leq \alpha<2$. Previous results have concentrated on the small-particle limit where the size of the attaching particle approaches zero in the limit. However, we consider the case where we rescale the whole cluster by its capacity before taking limits, whilst keeping the particle size fixed. We first consider the case where $\alpha=0$ and show that under capacity rescaling, the limiting structure of the cluster is not a disk, unlike in the small-particle limit. Then we consider the case where $0<\alpha<2$ and show that under the same rescaling the cluster approaches a disk. We also evaluate the fluctuations and show that, when represented as a holomorphic function, they behave like a Gaussian field dependent on $\alpha$. Furthermore, this field becomes degenerate as $\alpha$ approaches 0 and 2, suggesting the existence of phase transitions at these values.",
author = "George Liddle and Amanda Turner",
year = "2021",
month = may,
day = "31",
doi = "10.1214/20-AIHP1104",
language = "English",
volume = "57",
pages = "980--1015",
journal = "Annales de l'Institut Henri Poincar{\'e} (B) Probabilit{\'e}s et Statistiques",
issn = "0246-0203",
publisher = "Institute of Mathematical Statistics",
number = "2",

}

RIS

TY - JOUR

T1 - Scaling limits and fluctuations for random growth under capacity rescaling

AU - Liddle, George

AU - Turner, Amanda

PY - 2021/5/31

Y1 - 2021/5/31

N2 - We evaluate a strongly regularised version of the Hastings-Levitov model HL$(\alpha)$ for $0\leq \alpha<2$. Previous results have concentrated on the small-particle limit where the size of the attaching particle approaches zero in the limit. However, we consider the case where we rescale the whole cluster by its capacity before taking limits, whilst keeping the particle size fixed. We first consider the case where $\alpha=0$ and show that under capacity rescaling, the limiting structure of the cluster is not a disk, unlike in the small-particle limit. Then we consider the case where $0<\alpha<2$ and show that under the same rescaling the cluster approaches a disk. We also evaluate the fluctuations and show that, when represented as a holomorphic function, they behave like a Gaussian field dependent on $\alpha$. Furthermore, this field becomes degenerate as $\alpha$ approaches 0 and 2, suggesting the existence of phase transitions at these values.

AB - We evaluate a strongly regularised version of the Hastings-Levitov model HL$(\alpha)$ for $0\leq \alpha<2$. Previous results have concentrated on the small-particle limit where the size of the attaching particle approaches zero in the limit. However, we consider the case where we rescale the whole cluster by its capacity before taking limits, whilst keeping the particle size fixed. We first consider the case where $\alpha=0$ and show that under capacity rescaling, the limiting structure of the cluster is not a disk, unlike in the small-particle limit. Then we consider the case where $0<\alpha<2$ and show that under the same rescaling the cluster approaches a disk. We also evaluate the fluctuations and show that, when represented as a holomorphic function, they behave like a Gaussian field dependent on $\alpha$. Furthermore, this field becomes degenerate as $\alpha$ approaches 0 and 2, suggesting the existence of phase transitions at these values.

U2 - 10.1214/20-AIHP1104

DO - 10.1214/20-AIHP1104

M3 - Journal article

VL - 57

SP - 980

EP - 1015

JO - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

SN - 0246-0203

IS - 2

ER -