Freeness over the diagonal for large random matrices

Au, Benson, Cébron, Guillaume, Dahlqvist, Antoine, Gabriel, Franck and Male, Camille (2020) Freeness over the diagonal for large random matrices. Annals of Probablitiy. ISSN 0091-1798 (Accepted)

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Abstract

We prove that independent families of permutation invariant ran- dom matrices are asymptotically free with amalgamation over the diagonal, both in expectation and in probability, under a uniform boundedness assumption on the operator norm. We can relax the op- erator norm assumption to an estimate on sums associated to graphs of matrices, further extending the range of applications (for example, to Wigner matrices with exploding moments and the sparse regime of the Erdo ̈s-R ́enyi model). The result still holds even if the matrices are multiplied entrywise by random variables satisfying a certain growth condition (for example, as in the case of matrices with a variance profile and percolation models). Our analysis relies on a modified method of moments based on graph observables.

Item Type: Article
Keywords: Random matrices, Permutation invariance, Free Probability, Amalgamation
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
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Depositing User: Antoine Dahlqvist
Date Deposited: 12 May 2020 13:40
Last Modified: 12 May 2020 13:45
URI: http://sro.sussex.ac.uk/id/eprint/91222

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