Core Lexicon and Contagious Words

Abstract

We present the new empirical parameter $f_c$, the most probable usage frequency of a word in a language, computed via the distribution of documents over frequency $x$ of the word. This parameter allows for filtering the core lexicon of a language from the content words, which tend to be extremely frequent in some texts written in specific genres or by certain authors. Distributions of documents over frequencies for such words display long tails as $x>f_c$ representing a bunch of documents in which such words are used in abundance. Collections of such documents exhibit a percolation like phase transition as the coarse grain of frequency $Δf$ (flattening out the strongly irregular frequency data series) approaches the critical value $f_c$.