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arXiv · 1205.0796

The Zipf law for random texts with unequal probabilities of occurrence of letters and the Pascal pyramid

V. V. Bochkarev·E. Yu. Lerner
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Abstract

We model the generation of words with independent unequal probabilities of occurrence of letters. We prove that the probability $p(r)$ of occurrence of words of rank $r$ has a power asymptotics. As distinct from the paper published earlier by B. Conrad and M. Mitzenmacher, we give a brief proof by elementary methods and obtain an explicit formula for the exponent of the power law.

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V. V. Bochkarev, E. Yu. Lerner. 2012-05-03. The Zipf law for random texts with unequal probabilities of occurrence of letters and the Pascal pyramid. https://doi.org/10.3103/s1066369x12120031

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