Graphons, permutons and the Thoma simplex: three mod‐Gaussian moduli spaces - Laboratoire de Mathématiques d'Orsay
Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2020

Graphons, permutons and the Thoma simplex: three mod‐Gaussian moduli spaces

Résumé

In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three frameworks, a generic homogeneous observable of a generic random model is mod-Gaussian under an appropriate renormalization. This implies a central limit theorem with an extended zone of normality, a moderate deviation principle, an estimate of the speed of convergence, a local limit theorem and a concentration inequality. The universal asymptotic behavior of the observables of these models gives rise to a notion of mod-Gaussian moduli space.
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Dates et versions

hal-02998775 , version 1 (06-01-2025)

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Valentin Feray, Pierre‐loïc Méliot, Ashkan Nikeghbali. Graphons, permutons and the Thoma simplex: three mod‐Gaussian moduli spaces. Proceedings of the London Mathematical Society, 2020, 121 (4), pp.876-926. ⟨10.1112/plms.12344⟩. ⟨hal-02998775⟩
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