Asymptotic Eigenvalue Distributions of Block-Transposed Wishart Matrices

Teodor Banica () and Ion Nechita ()
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Teodor Banica: Cergy-Pontoise University
Ion Nechita: Université de Toulouse, UPS

Journal of Theoretical Probability, 2013, vol. 26, issue 3, 855-869

Abstract: Abstract We study the partial transposition W Γ=(id⊗t)W∈M dn (ℂ) of a Wishart matrix W∈M dn (ℂ) of parameters (dn,dm). Our main result is that, with d→∞, the law of mW Γ is a free difference of free Poisson laws of parameters m(n±1)/2. Motivated by questions in quantum information theory, we also derive necessary and sufficient conditions for these measures to be supported on the positive half-line.

Keywords: Wishart matrix; Partial transposition; Free Poisson law; 60B20; 46L54; 81P45 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-012-0409-4

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