TY - JOUR

T1 - Markov processes

T2 - Linguistics and Zipf's Law

AU - Kanter, I.

AU - Kessler, D. A.

PY - 1995

Y1 - 1995

N2 - 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/kρ, where ρ(k) is slowly increasing for small k; (b) the frequencies of occurrence of letters are given by P(k)=A-Dln(k); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.

AB - 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/kρ, where ρ(k) is slowly increasing for small k; (b) the frequencies of occurrence of letters are given by P(k)=A-Dln(k); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.

UR - http://www.scopus.com/inward/record.url?scp=0001153883&partnerID=8YFLogxK

U2 - 10.1103/physrevlett.74.4559

DO - 10.1103/physrevlett.74.4559

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AN - SCOPUS:0001153883

SN - 0031-9007

VL - 74

SP - 4559

EP - 4562

JO - Physical Review Letters

JF - Physical Review Letters

IS - 22

ER -