可加多步马氏链中词的秩分布与Zipf定律
Rank distributions of words in additive many-step Markov chains and the Zipf law
摘要：
本文将具有阶式记忆功能的二进制多步马尔可夫链作为分析随机符号动力系统中词的秩分布的模型。我们证明了，该分布的包络曲线服从幂律的单位阶指数的情况下，相当强的持续相关。齐普夫定律被证明是有效的词的秩分布的长度和短于马尔可夫序列中的相关长度。观察到的自相似性的秩分布相对于抽取过程。
英文摘要：
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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