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A central limit theorem for partial transposes of multipartite Wishart matrices

Part of: Special matrices Selfadjoint operator algebras

Published online by Cambridge University Press:  08 September 2025

Gyunam Park  and
Sang-Gyun Youn
Gyunam Park
Affiliation:
Department of Mathematics Education, Seoul National University, Gwanak-Ro 1, Gwanak-Gu, Seoul, Republic of Korea (pgn518@snu.ac.kr)
Sang-Gyun Youn*
Affiliation:
Department of Mathematics Education, Seoul National University, Gwanak-Ro 1, Gwanak-Gu, Seoul, Republic of Korea (s.youn@snu.ac.kr)
*
*Corresponding author.
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Abstract

The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [10] established asymptotic freeness between partial transposes in the bipartite situation. In this paper, we prove almost sure asymptotic freeness in the general multipartite situation and establish a central limit theorem for the partial transposes.

Keywords

partial transpositionmultipartite Wishart matrixasymptotic freenesscentral limit theorem

MSC classification

Primary: 46L54: Free probability and free operator algebras
Secondary: 15B52: Random matrices

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 38
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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