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Contribution Details

Type Journal Article
Scope Discipline-based scholarship
Title Graphons, Permutons and the Thoma simplex: three mod-Gaussian moduli spaces
Organization Unit
  • Ashkan Nikeghbali
  • Valentin Féray
  • Pierre-Loïc Méliot
Item Subtype Original Work
Refereed Yes
Status Published in final form
  • English
Journal Title Proceedings of the London Mathematical Society
Geographical Reach international
Volume 121
Number 4
Page Range 876 - 926
Date 2020
Abstract Text 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 renormalisation. 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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