The Random Division of the Unit Interval and the Approximate -1 Exponent in the Monkey-at-the-Typewriter Model of Zipf's Law

Richard Perline

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arXiv · 1512.02177

The Random Division of the Unit Interval and the Approximate -1 Exponent in the Monkey-at-the-Typewriter Model of Zipf's Law

Richard Perline

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Abstract

We show that the exponent in the inverse power law of word frequencies for the monkey-at-the-typewriter model of Zipf's law will tend towards -1 under broad conditions as the alphabet size increases to infinity and the letter probabilities are specified as the values from a random division of the unit interval. This is proved utilizing a strong limit theorem for log-spacings due to Shao and Hahn.

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Richard Perline. 2015-12-07. The Random Division of the Unit Interval and the Approximate -1 Exponent in the Monkey-at-the-Typewriter Model of Zipf's Law. https://arxiv.org/abs/1512.02177

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