V. V. Bochkarev, E. Yu. Lerner, “The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 12, 30–33; Russian Math. (Iz. VUZ), 56:12 (2012), 25

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 12, Pages 30–33 (Mi ivm8756)

This article is cited in 6 scientific papers (total in 6 papers)

The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid

V. V. Bochkarev^a, E. Yu. Lerner^b

^a Chair of Radiophysics, Kazan (Volga Region) Federal University, Kazan, Russia
^b Chair of Economic Cybernetics, Kazan (Volga Region) Federal University, Kazan, Russia

Full-text PDF (160 kB) Citations (6)

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Abstract: The model of word generation with independent unequal letter probabilities is analyzed in the article. It is proved that the probability

$p(r)$ of words of rank

$r$ has the power asymptotic behavior. Elementary methods not similar to Conrad and Mitzenmacher ones are used to represent a short proof of the theorem. We derive also an explicit formula of power.

Keywords: Zipf law, monkey model, order statistics, power laws, Pascal pyramid, recursive sequences, functional equations.

Received: 25.11.2011

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 12, Pages 25–27
DOI: https://doi.org/10.3103/S1066369X12120031

Bibliographic databases:

Document Type: Article

UDC: 519.213

Language: Russian

Citation: V. V. Bochkarev, E. Yu. Lerner, “The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 12, 30–33; Russian Math. (Iz. VUZ), 56:12 (2012), 25–27

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/ivm8756

https://www.mathnet.ru/eng/ivm/y2012/i12/p30

This publication is cited in the following 6 articles:

I. A. Belashova, V. V. Bochkarev, V. A. Tyurin, “Methods of verification of compliance with an asymptotically power law”, 6Th International Conference on Mathematical Modelling in Physical Sciences IC-MSQUARE 2017, Journal of Physics Conference Series, 936, IOP Publishing Ltd, 2017, UNSP 012074
V. V. Bochkarev, E. Yu. Lerner, A. A. Nikiforov, A. A. Pismenskiy, “Finding exact constants in a Markov model of Zipfs law generation”, 6Th International Conference on Mathematical Modelling in Physical Sciences IC-MSQUARE 2017, Journal of Physics Conference Series, 936, IOP Publishing Ltd, 2017, UNSP 012028
R. Perline, R. Perline, “Two universality properties associated with the monkey model of Zipf's law”, Entropy, 18:3 (2016)
Bochkarev V.V., Lerner E.Yu., “Strong Power and Subexponential Laws For An Ordered List of Trajectories of a Markov Chain”, Electron. J. Linear Algebra, 27 (2014), 534–556
Bochkarev V.V., Lerner E.Yu., “Zipf Exponent of Trajectory Distribution in the Hidden Markov Model”, 2Nd International Conference on Mathematical Modeling in Physical Sciences 2013 (Ic-Msquare 2013), Journal of Physics Conference Series, 490, eds. Vagenas E., Vlachos D., IOP Publishing Ltd, 2014, 012008
V. V. Bochkarev, E. Yu. Lerner, A. V. Shevlyakova, “Proverka zakona Khipsa po dannym korpusa Google Books Ngram”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2013, 16–23

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия высших учебных заведений. Математика

Russian Mathematics (Izvestiya VUZ. Matematika)

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