Header

UZH-Logo

Maintenance Infos

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.

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.

Statistics

Citations

Altmetrics

Downloads

0 downloads since deposited on 12 Oct 2020
0 downloads since 12 months

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Uncontrolled Keywords:General Mathematics
Language:English
Date:1 October 2020
Deposited On:12 Oct 2020 12:48
Last Modified:17 Nov 2020 04:39
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0024-6115
OA Status:Closed
Publisher DOI:https://doi.org/10.1112/plms.12344

Download

Closed Access: Download allowed only for UZH members