AI 中文总结
研究完全图中有向最小生成树形图的局部极限，证明其与均匀随机树局部极限相同，与最小生成树不同，揭示引入方向改变最小生成树局部几何结构。
AI 中文摘要
我们证明了完全图中最小生成树形图（它是完全图中最小生成树的有向类似物）的局部极限与朝向无穷的均匀随机树的局部极限相同。后者已知是条件生存的临界泊松高尔顿 - 沃森树。这与最小生成树的局部极限形成鲜明对比，已知其与均匀生成树的局部极限不同。因此我们证明了引入方向以一种不平凡的方式改变了最小生成树的局部几何结构。
英文摘要
We prove that the local limit of the minimum spanning arborescence in the complete graph (which is an oriented cousin of the minimum spanning tree in the complete graph) is the same as that of the uniform random tree, oriented towards infinity. The latter is known to be the critical Poisson Galton--Watson tree conditioned to survive. This is in sharp contrast with the local limit of the minimum spanning tree, which is known to be different from that of the uniform spanning tree (due to results of Addario--Berry \cite{AddarioBerry2013} and Addario--Berry, Griffiths and Kang \cite{PWIT_local_minimum}). Thus we demonstrate that introducing orientations changes the local geometry of the minimum spanning tree in a non-trivial manner.
Comments44 pages, many figures
