Second Order Cumulants of products
Operator Algebras
2009-05-22 v1 Probability
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.
Keywords
Cite
@article{arxiv.0708.0586,
title = {Second Order Cumulants of products},
author = {James A. Mingo and Roland Speicher and Edward Tan},
journal= {arXiv preprint arXiv:0708.0586},
year = {2009}
}
Comments
37 pages, 23 figures