For a solid-on-solid model of a driven interface, the paper proves that height fluctuations scale as N^(1/4) and converge to a stationary Ornstein-Uhlenbeck process with variance sigma/2.
Billingsley Convergence of Probability measures Wiley, New York, 1968
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Interface fluctuations in non equilibrium stationary states: the SOS approximation
For a solid-on-solid model of a driven interface, the paper proves that height fluctuations scale as N^(1/4) and converge to a stationary Ornstein-Uhlenbeck process with variance sigma/2.