ON THE SPECTRAL CRITERIA OF DISORDER IN NONPERIODIC SEQUENCES - APPLICATION TO INFLATION MODELS, SYMBOLIC DYNAMICS AND DNA-SEQUENCES

The spectral representation gives an effective approach to the analysis of statistical characteristics of symbolic sequences. We derive the corresponding criteria for the random case. The criteria ensure the dichotomic classification (random-non-random) for relatively short sequences of about several thousand symbols. The theory is applied to inflation models, symbolic dynamics and DNA sequences.