Second Order Cumulants of products

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.

37 pages, 23 figures

References in corpus (3)

• Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices
• Statistical eigen-inference from large Wishart matrices
• Second Order Freeness and Fluctuations of Random Matrices, III. Higher order freeness and free cumulants

Cited by in corpus (6)

• Asymptotics of unitary and othogonal matrix integrals
• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• Real Second Order Freeness and Haar Orthogonal Matrices
• Non-crossing Annular Pairings and The Infinitesimal Distribution of the GOE
• Schwinger-Dyson equations: classical and quantum
• Algebras with two multiplications and their cumulants