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  • 2008.05792v1

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Growth of Stationary Hastings-Levitov

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>31/10/2022
<mark>Journal</mark>Annals of Applied Probability
Issue number5
Number of pages32
Pages (from-to)3331-3330
Publication StatusPublished
Early online date18/10/22
<mark>Original language</mark>English


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.

Bibliographic note

32 pages, 2 figures