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

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.

4 pages

References in corpus (1)

• Zipf and non-Zipf Laws for Homogeneous Markov Chain

Cited by in corpus (1)

• Two Universality Properties Associated with the Monkey Model of Zipf's Law