Finite size effects in cluster-cluster aggregation

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Abstract
A finite size estimate is proposed for the fractal dimension of clusters obtained through hierarchical kinetic cluster-cluster aggregation. This estimate is shown to be exactly size-independent for d = 1 and above the upper critical dimension dc. For 1 < d < dc, it varies only weakly with size, leading to better values for the extrapolated fractal dimension, as shown by numerical results on Brownian and linear trajectories for 2 ≤ d ≤ 5