LONG-RANGE DEPENDENCE IN LEXICAL RENEWAL SERIES

Abstract

This work proposes a numerical series to describe the long-range structure of written texts: each word is mapped to one of four frequency classes, and the number of times the class changes from one position to the next is counted in successive blocks along the text. Classical Detrended Fluctuation Analysis (DFA) and its wavelet- and clustering-based variant (DFA-WK) are applied to this series, using a corpus of public-domain literary works. The resulting exponents indicate long-range dependence in most texts, a result confirmed by a control test involving word shuffling, which preserves the frequency distribution while destroying the original order. The exponent proved stable across genres, authors, and eras, yet it did not distinguish between texts with high and low lexical repetition; this suggests it captures a more general structural property of writing rather than serving as a measure of vocabulary richness. Since large language models learn the statistical regularities of text corpora, this long-range structure is a promising candidate property for comparing human-written text with machine-generated text, a possibility not tested here but rendered promising by the observed stability of the exponent.