Internal diffusion limited aggregation (internal DLA) is a cluster model in Z(d) where new points are added by starting random walkers at the origin and letting them run until they have found a new point to add to the cluster. It has been shown that the limiting shape of internal DLA. clusters is spherical. Here we show that for d greater than or equal to 2 the fluctuations are subdiffusive; in fact, that they are of order at most n(1/3), at least up to logarithmic corrections. More precisely, we show that for all sufficiently large n the cluster after m = [omega(d)n(d)] steps covers all points in the ball of radius n - n(1/3)(ln n)(2) and is contained in the ball of radius n + n(1/3)(ln n)(4). [References: 5]
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