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arXiv · 0905.1361

Diamond Aggregation

Wouter Kager·Lionel Levine
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Abstract

Internal diffusion-limited aggregation is a growth model based on random walk in Z^d. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in Z^2 for which the limiting shape is a diamond. Certain of these walks -- those with a directional bias toward the origin -- have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

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Wouter Kager, Lionel Levine. 2009-05-09. Diamond Aggregation. https://doi.org/10.1017/s030500411000006x

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