Poisson-Dirichlet scaling limits of Kemp's supertrees
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916275241877504 |
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| author | Stufler, Benedikt |
| author_facet | Stufler, Benedikt |
| contents | We determine the Gromov--Hausdorff--Prokhorov scaling limits and local limits of Kemp's $d$-dimensional binary trees and other models of supertrees. The limits exhibit a root vertex with infinite degree and are constructed by rescaling infinitely many independent stable trees or other spaces according to a function of a two-parameter Poisson--Dirichlet process and gluing them together at their roots. We discuss universality aspects of random spaces constructed in this fashion and sketch a phase diagram. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16456 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Poisson-Dirichlet scaling limits of Kemp's supertrees Stufler, Benedikt Probability Combinatorics We determine the Gromov--Hausdorff--Prokhorov scaling limits and local limits of Kemp's $d$-dimensional binary trees and other models of supertrees. The limits exhibit a root vertex with infinite degree and are constructed by rescaling infinitely many independent stable trees or other spaces according to a function of a two-parameter Poisson--Dirichlet process and gluing them together at their roots. We discuss universality aspects of random spaces constructed in this fashion and sketch a phase diagram. |
| title | Poisson-Dirichlet scaling limits of Kemp's supertrees |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2305.16456 |