AI 中文总结
本文确定了Hoffman有根树图的Martin边界，证明其由递归油漆盒参数化，并给出了递归Ewens族的极值分解。
AI 中文摘要
我们确定了Hoffman在有限无标号非平面有根树上的叶嫁接图的Doob-Martin边界。其全边界与最小边界重合，并由确定性递归油漆盒参数化，当它们的有限采样律一致时被识别。每个中心测度是相应极值律的唯一混合，其极限边界点生成完备的尾部域。我们还证明了该边界与由子边界类标记的无序根质量空间同胚。对于递归Ewens族，我们从独立的Poisson-Dirichlet分裂中获得了唯一的极值分解，包括均匀递归树和有根树Plancherel情形。
英文摘要
We determine the Doob-Martin boundary of Hoffman's leaf-grafting graph on finite unlabelled non-plane rooted trees. Its full and minimal boundaries coincide and are parametrized by deterministic recursive paintboxes, identified when their finite sampling laws agree. Every central measure is a unique mixture of the corresponding extremal laws, and its limiting boundary point generates the completed tail field. We also show that the boundary is homeomorphic to the space of unordered root masses marked by child boundary classes. For the recursive Ewens family, we obtain the unique extremal decomposition from independent Poisson-Dirichlet splits, including the uniform recursive-tree and rooted-tree Plancherel cases.
Comments48 pages
