A STOCHASTIC MODEL OF LANGUAGE CHANGE THROUGH SOCIAL STRUCTURE AND PREDICTION-DRIVEN INSTABILITY

Abstract. We develop a new stochastic model of language learn-ing and change that incorporates variable speech and age structure. Children detect correlations between age and speech, predict how the language is changing, and speak according to that prediction. Although the population tends to be dominated by one idealized grammar or another, the learning process amplifies chance corre-lation between age and speech, generating prediction-driven insta-bility and spontaneous language change. The model is formulated as a Markov chain, and a stochastic differential equation. It ex-hibits the abrupt monotonic shifts among equilibria characteristic of language changes. Fundamental results are proved. 1. The paradox of language change Language has both discrete and continuous characteristics. On the discrete side, most sentences are clearly either grammatical or ungram-matical. An idealized grammar is a formalism that identifies correct utterances, and much of the research on how children acquire their na-tive language focuses on how they might choose an idealized grammar from many innate possibilities on the basis of example sentences from Key words and phrases. language change; prediction-driven instability; popula-tion dynamics; stochastic differential equation; noise-activated transitions; AM