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}
}