## 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.## References

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## Additional Information

**James A. Mingo**- Affiliation: Department of Mathematics and Statistics, Jeffery Hall, Queen’s University, Kingston, Ontario, Canada K7L 3N6
- Email: mingo@mast.queensu.ca
**Roland Speicher**- Affiliation: Department of Mathematics and Statistics, Jeffery Hall, Queen’s University, Kingston, Ontario, Canada K7L 3N6
- Email: speicher@mast.queensu.ca
**Edward Tan**- Affiliation: Department of Mathematics and Statistics, Jeffery Hall, Queen’s University, Kingston, Ontario, Canada K7L 3N6
- Email: 3et8@qlink.queensu.ca
- Received by editor(s): August 17, 2007
- Published electronically: April 21, 2009
- Additional Notes: The research of the first and second authors was supported by Discovery Grants and a Leadership Support Initiative Award from the Natural Sciences and Engineering Research Council of Canada

The research of the second author was supported by a Killam Fellowship from the Canada Council for the Arts.

The research of the third author was supported by an Undergraduate Student Research Award from the Natural Sciences and Engineering Research Council of Canada - © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**361**(2009), 4751-4781 - MSC (2000): Primary 46L54; Secondary 15A52, 60F05
- DOI: https://doi.org/10.1090/S0002-9947-09-04696-0
- MathSciNet review: 2506426