Poisson–Dirichlet Scaling Limits of Kemp’s Supertrees

Benedikt Stufler ()
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Benedikt Stufler: Vienna University of Technology

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-29

Abstract: 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.

Keywords: Supertrees; Kemp’s multidimensional trees; Scaling limits; Random trees; Invariance principles; 60C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01419-8

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