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Subdiffusive fluctuations for internal diffusion limited aggregation. (English) Zbl 0835.60086
Internal diffusion limited aggregation is a cluster model in \(\mathbb{Z}^d\) which is formed by independent random walkers starting at the origin, which add the first point they visit, which is not yet contained in the cluster, to it. It was shown by the author with M. Bramson and D. Griffeath [Ann. Probab. 20, No. 4, 2117-2140 (1992; Zbl 0762.60096)] that the clusters have the limiting shape of a sphere. In the present paper it is shown that for \(d \geq 2\) the fluctuations are of order at most \(n^{1/3}\) up to logarithmic corrections, hence subdiffusive which had been suggested nonrigorously.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
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