Internal Diffusion Limited Aggregation on Discrete Groups Having Exponential Growth

Blachère, Sébastien; Brofferio, Sara

doi:10.1007/s00440-006-0009-2

Cited by 45 publications

(57 citation statements)

References 11 publications

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“…Blachère and Brofferio [3] obtained a limiting shape when the graph is a finitely generated group with exponential growth. Huss [10] studied internal DLA for a large class of random walks on such graphs.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations for internal DLA on the comb

Asselah¹,

Rahmani²

2016

Ann. Inst. H. Poincaré Probab. Statist.

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We study internal diffusion limited aggregation (DLA) on the two dimensional comb lattice. The comb lattice is a spanning tree of the euclidean lattice, and internal DLA is a random growth model, where simple random walks, starting one at a time at the origin of the comb, stop when reaching the first unoccupied site. An asymptotic shape is suggested by a lower bound of Huss and Sava [11]. We bound the fluctuations with respect to this shape.AMS 2010 subject classifications: 60K35, 82B24, 60J45.

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Section: Introductionmentioning

confidence: 99%

Fluctuations for internal DLA on the comb

Asselah¹,

Rahmani²

2016

Ann. Inst. H. Poincaré Probab. Statist.

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“…Indeed, the diamond shape of the layers does not play an important role in our arguments. Blachère and Brofferio [BB07] study internal DLA based on uniformly layered walks for which #L k grows exponentially, such as simple random walk on a regular tree. The resulting internal DLA clusters have the regular hexagon as their asymptotic shape.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Diamond aggregation

Kager¹,

Levine²

2010

Math. Proc. Camb. Phil. Soc.

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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 walksthose 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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“…The IDLA model has been extended in several contexts including drifted random walks [20], Cayley graphs of finitely generated groups [4,5,8,12] and random environments [9,22]. Another interesting growth model is provided by Richardson's model [21], which is defined as follows.…”

Section: Historical Introduction and Motivationmentioning

confidence: 99%