The limiting distributions of large heavy Wigner and arbitrary random matrices
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Centre National de la Recherche Scientifique [CNRS] | |
| dc.contributor.author | MALE, Camille | |
| dc.date.accessioned | 2024-04-04T02:24:34Z | |
| dc.date.available | 2024-04-04T02:24:34Z | |
| dc.date.created | 2012-09-11 | |
| dc.date.issued | 2016-10-14 | |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189825 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Grandes matrices aléatoires - ANR-08-BLAN-0311 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | -distribution | |
| dc.subject.en | free probability | |
| dc.subject.en | asymptotic freeness | |
| dc.subject.en | Wigner | |
| dc.subject.en | heavy-tailed random matrices | |
| dc.subject.en | Erdös-Renyi graphs | |
| dc.title.en | The limiting distributions of large heavy Wigner and arbitrary random matrices | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
| dc.subject.hal | Mathématiques [math]/Algèbres d'opérateurs [math.OA] | |
| dc.identifier.arxiv | 1209.2366 | |
| bordeaux.journal | Journal of Functional Analysis | |
| bordeaux.page | 46 | |
| bordeaux.volume | 271 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00733792 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00733792v1 | |
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