English

Poisson-Dirichlet graphons and permutons

Probability 2026-01-21 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.2601.14166,
  title  = {Poisson-Dirichlet graphons and permutons},
  author = {Benedikt Stufler},
  journal= {arXiv preprint arXiv:2601.14166},
  year   = {2026}
}
R2 v1 2026-07-01T09:12:46.965Z