MALE, Camille

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MALE, Camille
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]

Langue

Article de revue

Ce document a été publié dans

Journal of Functional Analysis. 2016-10-14, vol. 271, n° 1, p. 46

Elsevier

Résumé en anglais

The model of heavy Wigner matrices generalizes the classical ensemble of Wigner matrices: the sub-diagonal entries are independent, identically distributed along to and out of the diagonal, and the moments its entries are of order 1/N, where N is the size of the matrices. Adjacency matrices of Erdös-Renyi sparse graphs and matrices with properly truncated heavy tailed entries are examples of heavy Wigner matrices. We consider a family X_N of independent heavy Wigner matrices and a family Y_N of arbitrary random matrices, independent of X_N, with a technical condition (e.g. the matrices of Y_N are deterministic and uniformly bounded in operator norm, or are deterministic diagonal). We characterize the possible limiting joint *-distributions of (X_N,Y_N) in the sense of free probability. We find that they depend on more than the *-distribution of Y_N. We use the notion of distributions of traffics and their free product to quantify the information needed on Y_N and to infer the limiting distribution of (X_N,Y_N). We give an explicit combinatorial formula for joint moments of heavy Wigner and independent random matrices. When the matrices of Y_N are diagonal, we give recursion formulas for these moments. We deduce a new characterization of the limiting eigenvalues distribution of a single heavy Wigner.< Réduire

Mots clés en anglais

-distribution

free probability

asymptotic freeness

Wigner

heavy-tailed random matrices

Erdös-Renyi graphs

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189825

Project ANR

Grandes matrices aléatoires - ANR-08-BLAN-0311

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251