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Abstract
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Using new combinatorial techniques, we significantly improve previous results on
asymptotic distributions and asymptotic free independence relations of partial
transposes of Wishart random matrices. In particular, we give a necessary and
sufficient condition for the asymptotic free independence of partial transposes of
Wishart matrices with difference block sizes.
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Keywords
Wishart random matrices, partial transpose, free
independence
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Mathematical Subject Classification
Primary: 46L54
Secondary: 05A05, 15B52
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Milestones
Received: 9 June 2020
Revised: 21 January 2022
Accepted: 21 January 2022
Published: 14 July 2022
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