Sublogarithmic fluctuations for internal DLA
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Amine Asselah [1] ; Alexandre Gaudillière [2]
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[1] Université Paris-Est
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[2] Université de Provence
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 1, 2013, págs. 1160-1179
- Idioma: inglés
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Resumen
We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of order log(radius) [resp., log2(radius)]. Using the same approach, we improve the upper bound on the inner fluctuation to log(radius)−−−−−−−−−√ when d is larger than or equal to three. The inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation.
