Poisson-Dirichlet graphons and permutons

Benedikt Stufler

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arXiv · 2601.14166

Poisson-Dirichlet graphons and permutons

Benedikt Stufler

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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.

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Benedikt Stufler. 2026-01-20. Poisson-Dirichlet graphons and permutons. https://arxiv.org/abs/2601.14166

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