A toy model for DLA arm growth in a wedge

Oren Louidor; Chanwoo Oh; Eviatar B. Procaccia

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arXiv · 2208.09835

A toy model for DLA arm growth in a wedge

Oren Louidor·Chanwoo Oh·Eviatar B. Procaccia

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Abstract

In this paper, we consider a non-homogeneous discrete-time Markov chain which can be seen as a toy model for the growth of the arms of the DLA (Diffusion limited aggregation) process in a sub-linear wedge. It is conjectured that in a thin enough linear wedge there is only one infinite arm in the DLA cluster and we demonstrate this phenomenon in our model. The technique follows a bootstrapping argument, in which we iteratively prove ever faster growth rate.

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Oren Louidor, Chanwoo Oh, Eviatar B. Procaccia. 2022-08-21. A toy model for DLA arm growth in a wedge. https://arxiv.org/abs/2208.09835

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