Rank distributions of words in additive many-step Markov chains and the Zipf law

Details Rank distributions of words in additive many-step Markov chains and the Zipf law Rank distributions of words in additive many-step Markov chains and the Zipf law

2004-06-22

arxiv.org/abs/physics/0406099v1

Physics

History and Philosophy of Physics

4pages, 3 figures

Scientific paper

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.

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