A toy model for DLA arm growth in a wedge

2022/08/21 by Louidor, Oren, Oh, Chanwoo, Procaccia, Eviatar B.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2208.09835

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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