Strong asymptotic freeness for Wigner and Wishart matrices

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We prove that any non commutative polynomial of r independent copies of Wigner matrices converges a.s. towards the polynomial of r free semicircular variables in operator norm. This result extends a previous work of Haagerup and Thorbjornsen where GUE matrices are considered, as well as the classical asymptotic freeness for Wigner matrices (i.e. convergence of the moments) proved by Dykema. We also study the Wishart case.

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Probability, 15A52; 46L54; 60F99

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http://salesiana.dossiersoluciones.com/handle/123456789/74963

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504414
 http://arxiv.org/abs/math/0504414

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arXiv