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Pré-Publication, Document De Travail Année : 2011

Lower bounds on fluctuations for internal DLA

Résumé

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. When n random walks are sent from the origin, we establish a lower bound for the inner and outer errors fluctuations of order square root of the logarithm of n. When dimension is larger or equal to three, this lower bound matches the upper bound recently obtained in independent works of \cite{AG2} and \cite{JLS2}. Also, we produce as a corollary of our proof of \cite{AG2}, an upper bound for the fluctuation of the inner error in a specified direction.

Dates et versions

hal-00795848 , version 1 (01-03-2013)

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Amine Asselah, Alexandre Gaudilliere. Lower bounds on fluctuations for internal DLA. 2011. ⟨hal-00795848⟩
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