Decorated stable trees
Abstrak
We define decorated $α$-stable trees which are informally obtained from an $α$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $α$-stable looptrees of Curien and Kortchemski, where those metric spaces are just deterministic circles. We provide different constructions for these objects, which allows us to understand some of their geometric properties, including compactness, Hausdorff dimension and self-similarity in distribution. We prove an invariance principle which states that under some conditions, analogous discrete objects, random decorated discrete trees, converge in the scaling limit to decorated $α$-stable trees. We mention a few examples where those objects appear in the context of random trees and planar maps, and we expect them to naturally arise in many more cases.
Topik & Kata Kunci
Penulis (3)
Delphin Sénizergues
Sigurdur Örn Stefánsson
Benedikt Stufler
Akses Cepat
- Tahun Terbit
- 2022
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓