On the Limiting Empirical Measure of the sum of rank one matrices with log-concave distribution - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Studia Mathematica Année : 2009

On the Limiting Empirical Measure of the sum of rank one matrices with log-concave distribution

Résumé

We consider n × n real symmetric and hermitian random matrices Hn,m equals the sum of a non-random matrix H(0) matrix and the sum of m rank-one matrices determined by m i.i.d. isotropic random vectors with log-concave probability law and i.i.d. random amplitudes {τα}mα=1. This is a generalization of the case of vectors uniformly distributed over the unit sphere, studied in [17]. We prove as in [17] that if n → ∞, m → ∞, m/n → c ∈ [0,∞) and that the empirical eigenvalue measure of H(0) converges weakly, then the empirical eigenvalue measure of H converges in n n,m probability to a non-random limit, found in [17].
Fichier non déposé

Dates et versions

hal-00793742 , version 1 (22-02-2013)

Identifiants

  • HAL Id : hal-00793742 , version 1

Citer

Alain Pajor, Leonid Pastur. On the Limiting Empirical Measure of the sum of rank one matrices with log-concave distribution. Studia Mathematica, 2009, 195, pp.11-29. ⟨hal-00793742⟩
95 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More