Transactions of the American Mathematical Society

Author(s): James A. Mingo; Roland Speicher; Edward Tan
Journal: Trans. Amer. Math. Soc. 361 (2009), 4751-4781.
MSC (2000): Primary 46L54; Secondary 15A52, 60F05
Posted: April 21, 2009
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46L54, 15A52, 60F05

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

DOI: 10.1090/S0002-9947-09-04696-0
PII: S 0002-9947(09)04696-0
Received by editor(s): August 17, 2007
Posted: 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 of article: Copyright 2009, American Mathematical Society

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