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2020 Stabilization of DLA in a wedge
Eviatar B. Procaccia, Ron Rosenthal, Yuan Zhang
Electron. J. Probab. 25: 1-22 (2020). DOI: 10.1214/20-EJP446

Abstract

We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $\pi /4$, there is some $a>2$ such that almost surely, for all $R$ large enough, after time $R^{a}$ all new particles attached to the DLA will be at distance larger than $R$ from the origin. Furthermore, we provide estimates on the size of $R$ under which this holds. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process.

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Eviatar B. Procaccia. Ron Rosenthal. Yuan Zhang. "Stabilization of DLA in a wedge." Electron. J. Probab. 25 1 - 22, 2020. https://doi.org/10.1214/20-EJP446

Information

Received: 25 July 2019; Accepted: 9 March 2020; Published: 2020
First available in Project Euclid: 3 April 2020

zbMATH: 1441.60087
MathSciNet: MR4089792
Digital Object Identifier: 10.1214/20-EJP446

Subjects:
Primary: 60G50, 60K35, 60K40

JOURNAL ARTICLE
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