Multifractal Fourier spectra and power-law decay of correlations in random substitution sequences.
Binary symbolic sequences produced by randomly alternating substitution rules are considered. Exact expressions for the characteristics of autocorrelations and power spectra are derived. The decay of autocorrelation function obeys the power law. The Fourier spectral measure is either absolutely continuous or a mixture of the absolutely continuous and singular continuous components. For the latter case, the multifractal characteristics of this measure are computed.
Zaks
Michael A
MA
Institute of Physics, Potsdam University, PF 601553, D-14415 Potsdam, Germany.