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Freeness and The Partial Transposes of Wishart Random Matrices

  • James A. Mingo (a1) and Mihai Popa (a2) (a3)
Abstract

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.

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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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[8] Mingo, J. A. and Popa, M., Real second order freeness and Haar orthogonal matrices . J. Math. Phys. 54(2013), no. 5, 051701. https://doi.org/10.1063/1.4804168.
[9] Mingo, J. A. and Popa, M., Freeness and the transposes of unitarily invariant random matrices . J. Funct. Anal. 271(2016), 883921. https://doi.org/10.1016/j.jfa.2016.05.006.
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[13] Redelmeier, C. E. I., Real second-order freeness and the asymptotic real second-order freeness of several real matrix models. Int. Math. Res. Not. IMRN 2014, no. 12, 3353–3395.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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