Large permutation invariant random matrices are asymptotically free over the diagonal
MALE, Camille
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Article de revue
Ce document a été publié dans
Annals of Probability. 2020
Institute of Mathematical Statistics
Date de soutenance
2020Résumé en anglais
We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform boundedness assumption on the operator norm. ...Lire la suite >
We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform boundedness assumption on the operator norm. We can relax the operator 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 so the sparse regime of the Erdős-Rényi model). The result still holds even if the matrices are multiplied entrywise by bounded random variables (for example, as in the case of matrices with a variance profile and percolation models).< Réduire
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