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A Fock-space formalism is proposed which allows to get dynamical equations for averaged quantities from a master equation on a lattice with occupation numbers 0 and 1. Kinetic equations for restricted diffusion, non-penetrating diffusion-limited aggregation (DLA) and reaction-limited interface growth (RLA) are derived. We find a critical concentration of immobile particles above which diffusion disappears. The new DLA equations lead to a stable steady-state solution. As a special case of RLA the Kardar-Parisi-Zhang equation can be obtained.
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Sandow et al. (1993) studied this question.
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