Verification of the Heaps law using the Google Books Ngram database

This article is devoted to the verification of the Heaps empirical law for European languages using the Google Books Ngram corpus data. It is shown that the Heaps law holds only for short texts and texts related to short historical periods. The Heaps exponent decreases in time and varies significantly within characteristic intervals of 60–100 years. The relationship between the word frequency distribution and the expected dependence of the number of individual words on the text size is analyzed in terms of a simple probability model of text generation. This model serves as an explanation for the observed decreasing trend of the Heaps exponent.