相互作用创新过程的中心极限定理及相关统计工具和一般结果
Central limit theorems for interacting innovation processes, related statistical tools and general results
AI总结：
本文研究了相互作用创新过程的中心极限定理，提出了一种基于矩阵控制的创新触发和强化动态模型，并开发了统计工具用于推断过程间影响的结构和强度。
摘要：
我们研究了一个网络化的创新过程系统，其中每个过程被建模为一个具有无限多种颜色的 urn——一个经典的捕捉新颖性出现的框架。在此基础上，我们分析了一个相互作用 urn 模型，其中在一个过程生成或重用元素的概率受到其他过程历史的影响。这种相互作用由两个矩阵控制，分别控制创新触发和强化动态。本文的核心贡献是对该模型的二次渐进行为进行详细分析。基于这些理论结果，我们开发了统计工具来推断过程间影响的结构和强度。该方法被置于一个一般性设定中，使其具有广泛的应用性。我们通过两个现实世界的数据集——Reddit讨论和Gutenberg文本语料库的应用来验证我们的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
