Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Fluctuations for internal DLA on the comb

Amine Asselah and Houda Rahmani

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Abstract

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 (Electron. J. Probab. 17 (2012) 30). We bound the fluctuations with respect to this shape.

Résumé

Nous étudions un modèle d’agrégation limitée par diffusion interne (DLA), sur le peigne bidimensionnel. Le peigne est un arbre couvrant du réseau cubique, et DLA interne est un modèle de croissance aléatoire : des marches simples, lancées une après l’autre à l’origine du peigne, s’arrêtent lorsqu’elles atteignent le premier sommet inexploré. Une forme asymptotique est suggérée par une borne inférieure de Huss et Sava (Electron. J. Probab. 17 (2012) 30). Nous étudions les fluctuations par rapport à cette forme asymptotique.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 1 (2016), 58-83.

Dates
Received: 27 January 2014
Accepted: 21 June 2014
First available in Project Euclid: 6 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1452089260

Digital Object Identifier
doi:10.1214/14-AIHP629

Mathematical Reviews number (MathSciNet)
MR3449294

Zentralblatt MATH identifier
1335.60179

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B24: Interface problems; diffusion-limited aggregation 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Diffusion limited aggregation Cluster growth Random walk Shape theorem Lattice comb

Citation

Asselah, Amine; Rahmani, Houda. Fluctuations for internal DLA on the comb. Ann. Inst. H. Poincaré Probab. Statist. 52 (2016), no. 1, 58--83. doi:10.1214/14-AIHP629. https://projecteuclid.org/euclid.aihp/1452089260


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References

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