Yule–Simon-like models

Abstract This chapter discusses the foundational Yule–Simon model, which was the first general mechanism proposed to explain the emergence of Zipf’s law. The model is based on two key processes: innovation and reinforcement, often referred to as the ‘rich-get-richer’ effect. While this framework effectively produces power-law distributions, its limitations are acknowledged, particularly its inability to account for the sub-linear growth described by Heaps’ law. The chapter also explores a modification that incorporates a time-dependent innovation rate; however, this extension still does not fully explain the entire range of empirical laws, such as Taylor’s law.