A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of transmission events and thereby requires no time dependence of system properties. The waiting time distribution with a characteristic long tail gives rise to a nonstationary response in the presence of a voltage pulse. We report on noise measurements that

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... e well with the predicted non-Poissonian fluctuations in current, and discuss possible mechanisms leading to this behavior.