  The binary many-step Markov chain with the step-like memory function is
considered as a model for the analysis of rank distributions of words in
stochastic symbolic dynamical systems. We prove that the envelope curve for
this distribution obeys the power law with the exponent of the order of unity
in the case of rather strong persistent correlations. The Zipf law is shown to
be valid for the rank distribution of words with lengths about and shorter than
the correlation length in the Markov sequence. A self-similarity in the rank
distribution with respect to the decimation procedure is observed.
