Author:
KAGER WOUTER,LEVINE LIONEL
Abstract
AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 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.
Publisher
Cambridge University Press (CUP)
Cited by
2 articles.
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1. Fluctuations for internal DLA on the comb;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2016-02-01
2. Logarithmic fluctuations for internal DLA;Journal of the American Mathematical Society;2011-08-15