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Poisson-Dirichlet Graphons and Permutons

Author Benedikt Stufler

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LIPIcs.AofA.2026.11.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Trees
  • Mathematics of computing → Discrete mathematics
  • Mathematics of computing → Distribution functions
  • Mathematics of computing → Generating functions
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Combinatorics
Keywords
  • Graphons
  • Permutons
  • Poisson-Dirichlet point processes

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Abstract

We introduce classes of supergraphs and superpermutations with novel universal graphon and permuton limiting objects whose construction involves the two-parameter Poisson-Dirichlet process introduced by Pitman and Yor (1997). We demonstrate the universality of these limiting objects through general invariance principles in a heavy-tailed regime and establish a comprehensive phase diagram for the asymptotic shape of superstructures.

Cite As Get BibTex

Benedikt Stufler. Poisson-Dirichlet Graphons and Permutons. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AofA.2026.11

Author Details

Benedikt Stufler
  • TU Wien, Austria

Funding

This research was funded in part by the Austrian Science Fund (FWF) 10.55776/PAT6732623 and 10.55776/PAT1382025. For open access purposes, the authors have applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission.

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