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

Féray, Valentin; Méliot, Pierre‐Loïc; Nikeghbali, Ashkan (2020). Graphons, permutons and the Thoma simplex: three mod‐Gaussian moduli spaces. Proceedings of the London Mathematical Society, 121(4):876-926.

Abstract

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.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Finance
07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Uncontrolled Keywords:General Mathematics
Scope:Discipline-based scholarship (basic research)
Language:English
Date:1 October 2020
Deposited On:12 Oct 2020 12:48
Last Modified:24 Oct 2024 01:35
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0024-6115
OA Status:Closed
Publisher DOI:https://doi.org/10.1112/plms.12344
Other Identification Number:merlin-id:20023

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