Vol. 317, No. 2, 2022

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The partial transpose and asymptotic free independence for Wishart random matrices, II

James A. Mingo and Mihai Popa

Vol. 317 (2022), No. 2, 387–421
Abstract

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.

Keywords
Wishart random matrices, partial transpose, free independence
Mathematical Subject Classification
Primary: 46L54
Secondary: 05A05, 15B52
Milestones
Received: 9 June 2020
Revised: 21 January 2022
Accepted: 21 January 2022
Published: 14 July 2022
Authors
James A. Mingo
Department of Mathematics and Statistics
Queen’s University
Kingston, ON
Canada
Mihai Popa
Department of Mathematics
The University of Texas at San Antonio
San Antonio, TX
United States
“Simon Stoilow” Institute of Mathematics of the Romanian Academy
Bucharest
Romania