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If Γ is a random variable with values in a compact matrix group K, then the traces Tr(Γj) (j ∊ N) are real or complex valued random variables. As a crucial step in their approach to random matrix eigenvalues, Diaconis and Shahshahani computed the joint moments of any fixed number of these traces if Γ is distributed according to Haar measure and if K is one of Un, On or Spn, where n is large enough...
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