Abstract
We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t −β,β⩽1) or a compressed exponential decay [exp(−t α),α>1].
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Takayasu, H., Takayasu, M., Provata, A. et al. Statistical properties of aggregation with injection. J Stat Phys 65, 725–745 (1991). https://doi.org/10.1007/BF01053751
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DOI: https://doi.org/10.1007/BF01053751