Third order moments of complex Wigner matrices
Abstract
We compute the third order moments of a complex Wigner matrix. We provide a formula for the third order moments αm1,m2,m3 in terms of quotient graphs Tm1,m2,m3π where π is the Kreweras complement of a non-crossing pairing on the annulus. We prove that these graphs can be counted using the set of partitioned permutations, this permits us to write the third order moments in terms of the high order free cumulants which have a simple expression.
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