有限祖先有向无环图上的交互瓮方案
Interacting Urn Schemes on Finite Ancestral Directed Acyclic Graphs
浏览论文内容
中文总结 AI 辅助
本文研究有限祖先有向无环图上的交互有限色瓮方案，证明了瓮比例的几乎必然收敛性，确定了极限构型的决定顶点，并在强化矩阵满足特定假设下得到二阶渐近结果。
中文摘要 AI 辅助
我们研究有向无环图上的交互有限色瓮方案，允许该图为无限图。每个瓮通过与其入邻接瓮抽取的颜色驱动的强化过程演化，该过程依赖边相关的强化矩阵。假设每个顶点仅有有限个祖先，我们证明瓮比例的几乎必然收敛性，并表明极限构型由无祖先或无自环的顶点决定。在强化矩阵满足额外平衡与不可约性假设下，我们还在适当定义参数的所有范围内获得了二阶渐近结果。
英文摘要
We study interacting finite-color urn schemes on directed acyclic graphs, allowing the graph to be infinite. Each urn evolves through reinforcements driven by colors drawn from its in-neighboring urns via edge-dependent reinforcement matrices. Assuming that every vertex has only finitely many ancestors, we prove almost sure convergence of urn proportions and show that the limiting configuration is determined by vertices with no ancestors or self-loops. Under additional balance and irreducibility assumptions on reinforcement matrices, we also obtain second-order asymptotic results in all regimes of appropriately defined parameters.
