MARKOV-PROCESSES - LINGUISTICS AND ZIPFS LAW
MARKOV-PROCESSES - LINGUISTICS AND ZIPFS LAW
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DOI：
10.1103/physrevlett.74.4559
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发表时间：
1995-05-29
影响因子：
8.6
通讯作者：
KESSLER, DA
中科院分区：
文献类型：
--
作者：
KANTER, I;KESSLER, DA
结果表明，由N个状态和有偏随机跃迁构造的2参数随机马尔可夫过程可以得到一个平稳分布，其中状态P (k)、k= 1、…、N的出现概率表现出生物序列和自然语言文本的三个普遍特征：(a)单词的出现频率由齐夫定律P (k)∝1/k ρ给出，其中ρ (k)随着k的减小而缓慢增加；(b)字母出现的频率由P (k)= A−D ln (k)给出；(c)由于马尔可夫过程的准顺性，在长但有限的间隔内观察到远程相关性。
It is shown that a 2-parameter random Markov process constructed with N states and biased random transitions gives rise to a stationary distribution where the probabilities of occurrence of the states, P (k), k= 1,…, N, exhibit the following three universal behaviors which characterize biological sequences and texts in natural languages:(a) the rank-ordered frequencies of occurrence of words are given by Zipf's law P (k)∝ 1/k ρ, where ρ (k) is slowly increasing for small k;(b) the frequencies of occurrence of letters are given by P (k)= A− D ln (k); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.