GROWTH OF STATIONARY HASTINGS–LEVITOV

Noam Berger; Eviatar B. Procaccia; Amanda Turner

doi:https://doi.org/10.1214/21-AAP1761

GROWTH OF STATIONARY HASTINGS–LEVITOV

Noam Berger, Eviatar B. Procaccia, Amanda Turner

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3331-3360
Number of pages	30
Journal	Annals of Applied Probability
Volume	32
Issue number	5
DOIs	https://doi.org/10.1214/21-AAP1761
State	Published - Oct 2022

Keywords

Aggregation processes
DLA
Hastings–Levitov

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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https://doi.org/10.1214/21-AAP1761

Cite this

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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 n2/3, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.",

keywords = "Aggregation processes, DLA, Hastings–Levitov",

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

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2022.",

year = "2022",

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doi = "https://doi.org/10.1214/21-AAP1761",

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AU - Berger, Noam

AU - Procaccia, Eviatar B.

AU - Turner, Amanda

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2022.

PY - 2022/10

Y1 - 2022/10

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 n2/3, 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 n2/3, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.

KW - Aggregation processes

KW - DLA

KW - Hastings–Levitov

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U2 - https://doi.org/10.1214/21-AAP1761

DO - https://doi.org/10.1214/21-AAP1761

M3 - مقالة

SN - 1050-5164

VL - 32

SP - 3331

EP - 3360

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 5

ER -

GROWTH OF STATIONARY HASTINGS–LEVITOV

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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