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Operator valued random matrices and asymptotic freeness

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 نشر من قبل Weihua Liu
 تاريخ النشر 2018
  مجال البحث
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 تأليف Weihua Liu




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We show that the limit laws of random matrices, whose entries are conditionally independent operator valued random variables having equal second moments proportional to the size of the matrices, are operator valued semicircular laws. Furthermore, we prove an operator valued analogue of Voiculescus asymptotic freeness theorem. By replacing conditional independence with Boolean independence, we show that the limit laws of the random matrices are Operator-valued Bernoulli laws.



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