Central limit theorems for interacting innovation processes, related statistical tools and general results

We study a networked system of innovation processes, where each process is modeled as an urn with infinitely many colors-a classical framework for capturing the emergence of novelties. Ex- tending this paradigm, we analyze a model of interacting urns, where the probability of generating or reusing elements in one process is influenced by the histories of others. This interaction is gov- erned by two matrices that control innovation triggering and reinforcement dynamics across the system. The core contribution of this work is a detailed analysis of the second-order asymptotic behavior of the model. Building on these theoretical results, we develop statistical tools to infer the structure and strength of inter-process influence. The methodology is framed in a general set- ting, making it broadly applicable. We validate our approach with applications to two real-world datasets from Reddit discussions and Gutenberg text corpora.