Second order cumulants of products

Mingo, James; Speicher, Roland; Tan, Edward

doi:10.1090/S0002-9947-09-04696-0

Second order cumulants of products
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by James A. Mingo, Roland Speicher and Edward Tan PDF

Trans. Amer. Math. Soc. 361 (2009), 4751-4781 Request permission

Abstract:

We derive a formula which expresses a second order cumulant whose entries are products as a sum of cumulants where the entries are single factors. This extends to the second order case the formula of Krawczyk and Speicher. We apply our result to the problem of calculating the second order cumulants of a semi-circular and Haar unitary operator.

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