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Pré-Publication, Document De Travail Année : 2010

From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models

Résumé

We consider a family of cluster growth models on the d-dimensional lattice that generalize the internal diffusion limited aggregation (internal DLA). The latter model is the simplest to describe: random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. In this case, it is known that the asymptotic shape of the cluster is a sphere, and when dimension is 2 or more, the fluctuations of its radius are at most of order of the radius to the power 1/3. For our cluster growth models, we obtain upper and lower bounds for the inner and outer deviation probabilities from the asymptotic shape. Since our growth models are all coupled to internal DLA, we obtain that fluctuations for internal DLA are at most a power of log(n) in dimension d larger than or equal to 2.
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Dates et versions

hal-00517593 , version 1 (15-09-2010)
hal-00517593 , version 2 (04-12-2011)
hal-00517593 , version 3 (31-05-2013)

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Amine Asselah, Alexandre Gaudilliere. From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models. 2010. ⟨hal-00517593v1⟩
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