Distinguishing fractional and white noise in one and two dimensions.

@article{Hansen2001DistinguishingFA,
  title={Distinguishing fractional and white noise in one and two dimensions.},
  author={A. Hansen and Jean Schmittbuhl and G. G. Batrouni},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2001},
  volume={63 6 Pt 1},
  pages={
          062102
        }
}
We discuss the link between uncorrelated noise and the Hurst exponent for one- and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent H lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analyzing the correlations in two dimensions is necessary. For H>-1/2, a crossover regime leads to… 

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