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2018 Weighted dependency graphs
Valentin Féray
Electron. J. Probab. 23: 1-65 (2018). DOI: 10.1214/18-EJP222

Abstract

The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context. We also provide generic tools to prove that some weighted graph is a weighted dependency graph for a given family of random variables.

To illustrate the power of the theory, we give applications to the following objects: uniform random pair partitions, the random graph model $G(n,M)$, uniform random permutations, the symmetric simple exclusion process and multilinear statistics on Markov chains. The application to random permutations gives a bivariate extension of a functional central limit theorem of Janson and Barbour. On Markov chains, we answer positively an open question of Bourdon and Vallée on the asymptotic normality of subword counts in random texts generated by a Markovian source.

Citation

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Valentin Féray. "Weighted dependency graphs." Electron. J. Probab. 23 1 - 65, 2018. https://doi.org/10.1214/18-EJP222

Information

Received: 17 July 2017; Accepted: 9 September 2018; Published: 2018
First available in Project Euclid: 18 September 2018

zbMATH: 06964787
MathSciNet: MR3858921
Digital Object Identifier: 10.1214/18-EJP222

Subjects:
Primary: 60F05
Secondary: 05C80, 60C05, 60J10, 82C05

JOURNAL ARTICLE
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Vol.23 • 2018
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