Diamond aggregation

• Autores: Wouter Kager, Lionel Levine
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 149, Nº 2, 2010, págs. 351-372
• Idioma: inglés
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• Resumen

  • Internal 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.