Distinguishing fractional and white noise in one and two dimensions

Abstract

We discuss the link between uncorrelated noise and 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 lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analysing the correlations in two dimensions is necessary. For Hurst exponents larger than -1/2, a crossover regime leads to a systematic over estimate of the Hurst exponent.

3 pages RevTeX, 4 Postscript figures

References in corpus (2)

• Wave scattering from self-affine surfaces
• Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

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