The Random Division of the Unit Interval and the Approximate -1 Exponent in the Monkey-at-the-Typewriter Model of Zipf's Law
arXiv:1512.02177
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.
7 pages and 1 figure