Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Zhang, Shengjun
Institutions: Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214318833