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Research output: Contribution to journal › Journal article › peer-review

Forthcoming

**Growth of Stationary Hastings-Levitov.** / Berger, Noam; Procaccia, Eviatar B.; Turner, Amanda.

Research output: Contribution to journal › Journal article › peer-review

Berger, N, Procaccia, EB & Turner, A 2021, 'Growth of Stationary Hastings-Levitov', *Annals of Applied Probability*.

Berger, N., Procaccia, E. B., & Turner, A. (Accepted/In press). Growth of Stationary Hastings-Levitov. *Annals of Applied Probability*.

Berger N, Procaccia EB, Turner A. Growth of Stationary Hastings-Levitov. Annals of Applied Probability. 2021 Oct 21.

@article{2a4c2a96bb174ce193385ce2fd267a9c,

title = "Growth of Stationary Hastings-Levitov",

abstract = "We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment. ",

keywords = "math.PR, math-ph, math.MP",

author = "Noam Berger and Procaccia, {Eviatar B.} and Amanda Turner",

note = "32 pages, 2 figures",

year = "2021",

month = oct,

day = "21",

language = "English",

journal = "Annals of Applied Probability",

issn = "1050-5164",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Growth of Stationary Hastings-Levitov

AU - Berger, Noam

AU - Procaccia, Eviatar B.

AU - Turner, Amanda

N1 - 32 pages, 2 figures

PY - 2021/10/21

Y1 - 2021/10/21

N2 - We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.

AB - We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.

KW - math.PR

KW - math-ph

KW - math.MP

M3 - Journal article

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

ER -