  In his pioneering research, G. K. Zipf observed that more frequent words tend
to have more meanings, and showed that the number of meanings of a word grows
as the square root of its frequency. He derived this relationship from two
assumptions: that words follow Zipf's law for word frequencies (a power law
dependency between frequency and rank) and Zipf's law of meaning distribution
(a power law dependency between number of meanings and rank). Here we show that
a single assumption on the joint probability of a word and a meaning suffices
to infer Zipf's meaning-frequency law or relaxed versions. Interestingly, this
assumption can be justified as the outcome of a biased random walk in the
process of mental exploration.
