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arXiv · 1804.04236

Stabilization of DLA in a wedge

Eviatar B. Procaccia·Ron Rosenthal·Yuan Zhang
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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. 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. 2018-04-11. Stabilization of DLA in a wedge. https://arxiv.org/abs/1804.04236

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