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Freeness and The Partial Transposes of Wishart Random Matrices

Published online by Cambridge University Press:  09 January 2019

James A. Mingo
Affiliation:
Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, Kingston, Ontario K7L 3N6 Email: [email protected]
Mihai Popa
Affiliation:
Department of Mathematics, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, RO-70700, Romania Email: [email protected]
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Abstract

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We show that the partial transposes of complex Wishart random matrices are asymptotically free. We also investigate regimes where the number of blocks is fixed but the size of the blocks increases. This gives an example where the partial transpose produces freeness at the operator level. Finally, we investigate the case of real Wishart matrices.

Type
Article
Copyright
© Canadian Mathematical Society 2018 

Footnotes

Research of both authors was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Research of author M.P. was also supported by the Simons Foundation, grant No. 360242.

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