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

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