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. Extending 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 governed 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 setting, making it broadly applicable. We validate our approach with applications to two real-world datasets from Reddit discussions and Gutenberg text corpora.

翻译：本研究探讨创新过程的网络化系统，其中每个过程被建模为具有无限多种颜色的瓮模型——这是描述新颖性涌现的经典框架。通过扩展该范式，我们分析了一种交互式瓮模型，其中单个过程生成或复用元素的概率受到其他过程历史的影响。这种交互作用由两个矩阵控制，分别调控系统内的创新触发机制与强化动态。本工作的核心贡献在于对模型二阶渐近行为的详细分析。基于这些理论结果，我们开发了统计工具以推断过程间影响的结构与强度。该方法建立于一般性框架中，具有广泛的适用性。我们通过Reddit讨论和古腾堡文本语料库的两个真实数据集验证了所提方法的有效性。