TITLE

On the asymptotic distribution of block-modified random matrices

AUTHOR(S)
Arizmendi, Octavio; Nechita, Ion; Vargas, Carlos
PUB. DATE
January 2016
SOURCE
Journal of Mathematical Physics;2016, Vol. 57 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operatorvalued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations.
ACCESSION #
112728914

 

Related Articles

  • Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle. Krasovsky, I. V. // IMRN: International Mathematics Research Notices;2004, Vol. 2004 Issue 25, p1249 

    We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large s asymptotic expansion for the Fredholm determinant with the kernel sinz/(Ï€ z) on the interval [0,s],...

  • Eigenvectors of some large sample covariance matrix ensembles. Ledoit, Olivier; Péché, Sandrine // Probability Theory & Related Fields;Jul2011, Vol. 151 Issue 1/2, p233 

    We consider sample covariance matrices $${S_N=\frac{1}{p}\Sigma_N^{1/2}X_NX_N^* \Sigma_N^{1/2}}$$ where X is a N × p real or complex matrix with i.i.d. entries with finite 12th moment and Σ is a N × N positive definite matrix. In addition we assume that the spectral measure of Σ...

  • Precise asymptotics for random matrices and random growth models. Su, Zhong Gen // Acta Mathematica Sinica;Jun2008, Vol. 24 Issue 6, p971 

    The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of...

  • Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential. Saad, Nasser; Hall, Richard L.; Çiftçi, Hakan; Yeşiltaş, Özlem // Advances in Mathematical Physics;2011, p1 

    We study the generalized quantum isotonic oscillator Hamiltonian given by H=-d²/dr² + l(l + 1)/r²+w²r²+2g(r²-a²)/(r² + a²)²,g > 0. Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these...

  • Limits of spiked random matrices I. Bloemendal, Alex; Virág, Bálint // Probability Theory & Related Fields;Aug2013, Vol. 156 Issue 3/4, p795 

    Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in the rank one spiked real Wishart setting and its general...

  • ASYMPTOTICALLY STABLE SETS AND THE STABILITY OF w-LIMIT SETS. D'Aniello, Emma // Real Analysis Exchange;June2004 Conference Report, p31 

    Discusses the properties of asymptotically stable sets. Standard notations; Theorems.

  • Formal asymptotics of eigenmodes for oscillating elastic spatial bodies with concentrated masses. Gomez, D.; Nazarov, S.; Perez, M.-E. // Journal of Mathematical Sciences;Feb2008, Vol. 148 Issue 5, p650 

    Limit spectral problems are derived for the problem on oscillations of a solid with small heavy (or light) inclusions. The asymptotic ansatzs for eigenvalues and eigenvectors, as well as the limit problems, are crucially dependent on both the relation between the geometric and physical...

  • Asymptotic distribution of the eigenvalues and eigenfunctions in basic boundary value oscillation problems in hemitropic elasticity. Bezhuashvili, Yu.; Rukhadze, R. // Computational Mathematics & Mathematical Physics;Jul2013, Vol. 53 Issue 7, p984 

    The basic boundary value oscillation problems for a three-dimensional elastic medium bounded by a closed surface are considered. Asymptotic formulas are derived for the eigenvalue and eigenfunction distributions in the problems.

  • A note on the eigenvalues of $$g$$ -circulants (and of $$g$$ -Toeplitz, $$g$$ -Hankel matrices). Serra-Capizzano, Stefano; Sesana, Debora // Calcolo;Dec2014, Vol. 51 Issue 4, p639 

    A matrix $$A$$ of size $$n$$ is called $$g$$ -circulant if $$A=[a_{(r-g s)\text { mod } n}]_{r,s=0}^{n-1}$$ , while a matrix $$A$$ is called $$g$$ -Toeplitz if its entries obey the rule $$A=[a_{r-g s}]_{r,s=0}^{n-1}$$ . In this note we study the eigenvalues of $$g$$ -circulants and we provide a...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics