Operator-valued free Fisher information of random matrices

DOI10.1016/S0252-9602(10)60128-2zbMATH Open1240.46096arXivmath/0601527OpenAlexW1593338319MaRDI QIDQ551436

Bin Meng

Publication date: 19 July 2011

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Abstract: We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for $Ph{i}^{a}s{t}_{M_2(mb)}(A,A^{a}st,M_2(mb),eta)$, where $Ain{M}_2(mb)$ is a $2imes2$ operator matrix on $mb$, and $eta$ is linear operators on $M_2(mb)$. Then we consider a special setting: $A$ is an operator-valued semicircular matrix with conditional expectation covariance, and find that $Ph{i}_m{b}^{a}st(c,c^{a}st:mb,id)=2Index(E)$, where $E$ is a conditional expectation of $mb$ onto $md$ and $c$ is a circular variable with covariance $E$.

Full work available at URL: https://arxiv.org/abs/math/0601527

zbMATH Keywords

random matrixfree Fisher informationconjugate variablemodular frame

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) General harmonic expansions, frames (42C15) Random matrices (algebraic aspects) (15B52)

Related Items (2)

On finite free Fisher information for eigenvectors of a modular operator ⋮ Some minimization problems for the free analogue of the Fisher information

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