Geodesic
The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 30-33.

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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, recursive sequences, functional equations.
Mots-clés : Pascal pyramid 
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V. V. Bochkarev; E. Yu. Lerner. The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 30-33. http://geodesic.mathdoc.fr/item/IVM_2012_12_a2/

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