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

2004/06/22 by K. E. Kechedzhy O. V. Usatenko, K. E. Kechedzhy O.V. Usatenko, Usatenko, K. E. Kechedzhy O. V. +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Data Analysis #FOS: Physical sciences #Fractal and DNA sequence analysis #History and Philosophy of Physics (physics.hist-ph) #Protein Structure and Dynamics #Statistics and Probability (physics.data-an) #Stochastic processes and statistical mechanics #physics.data-an #physics.hist-ph

paper · pdf · doi:10.48550/arxiv.physics/0406099

4pages, 3 figures

arxiv created 2004/06/22 · openalex publication_date 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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