Talk by Alessandro Bellina

Since George Polya’s initial introduction in 1930, Urn Models have found applications across diverse fields, including biology, economics, and sociology. Recently, these simplistic models have been endowed by the Theory of Adjacent Possibilities, which proposes that the space of potential exploration expands every time a new element is discovered. This concept has led to the development of Urn models with Triggering, widely used to simulate the dynamics of novelty and innovation, where Heaps’ and Zipf’s laws are typically observed. However, two primary limitations of this framework deserve consideration. Firstly, novelties and innovations frequently emerge as recombinations of existing elements, necessitating analysis of higher-order novelty dynamics. Secondly, the mechanisms driving novelties are typically non-stationary, suggesting the need for time-dependent dynamics in the standard Urn Model with Triggering. In this presentation, I will discuss concrete applications of these concepts, which can offer a more realistic representation of certain phenomena.