This article is cited in 6 papers

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

V. V. Bochkarev^a, E. Yu. Lerner<sup>b

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

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.

UDC: 519.213

Received: 25.11.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:12, 25–27

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