Probability distribution of the interface width in surface roughening: Analogy with a Levy flight

The authors present a closed-form expression for the probability distribution of the height fluctuations in the Zhang model of anomalous surface roughening. The result-which includes both the steady state behavior and the time evolution to the steady state-is based on an analogy between the (d=1+1)-dimensional 'surface' problem and a d=1 Levy flight. In the limit case of conventional ballistic deposition they obtain a Gaussian distribution for the height fluctuations. Their results are corroborated by detailed numerical simulations.