Growth of Stationary Hastings-Levitov

Berger, Noam and Procaccia, Eviatar B. and Turner, Amanda (2022) Growth of Stationary Hastings-Levitov. Annals of Applied Probability, 32 (5). pp. 3331-3330. ISSN 1050-5164

[thumbnail of 2008.05792v1]
Text (2008.05792v1)
2008.05792v1.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (1MB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Annals of Applied Probability
Additional Information:
32 pages, 2 figures
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
?? math.prmath-phmath.mpstatistics and probabilitystatistics, probability and uncertainty ??
ID Code:
146814
Deposited By:
Deposited On:
26 Aug 2020 08:15
Refereed?:
Yes
Published?:
Published
Last Modified:
12 Mar 2024 00:51