Poisson-Dirichlet scaling limits of Kemp's supertrees

Benedikt Stufler

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arXiv · 2305.16456

Poisson-Dirichlet scaling limits of Kemp's supertrees

Benedikt Stufler

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Abstract

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.

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Benedikt Stufler. 2023-05-25. Poisson-Dirichlet scaling limits of Kemp's supertrees. https://arxiv.org/abs/2305.16456

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