No Eigenvalues Outside The Support

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No Eigenvalues Outside the Support of the Limiting ...

    https://jack.math.ncsu.edu/noeigenvalues.pdf
    (1998) and Paul and Silverstein (2007), the nonexistence of eigenvalues outside the support of F. It is necessary at this point to review some of the properties of F and m F, obtained in Dozier and Silverstein (2007b). It is shown that for all x2R f 0g, lim z2C+!xm F(z) m 0(x) exists. From this it follows that Fhas a continuous derivative

No Eigenvalues Outside the Limiting Support of Generally ...

    https://repository.kaust.edu.sa/bitstream/handle/10754/610651/07464912.pdf?sequence=1&isAllowed=y
    under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this …

NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING ...

    https://www.worldscientific.com/doi/10.1142/S2010326311500043
    In this paper we show that, under certain conditions on R n, for any closed interval in ℝ + outside the support of the limiting distribution, then, almost surely, no eigenvalues of …Cited by: 25

Bai , Silverstein : No eigenvalues outside the support of ...

    https://projecteuclid.org/euclid.aop/1022855421
    No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Z. D. Bai and Jack W. Silverstein

No eigenvalues outside the support of the limiting ...

    https://www.sciencedirect.com/science/article/pii/S0047259X08001024
    We show that, under appropriate conditions on the eigenvalues of A n and B n, with probability 1, there will be no eigenvalues in any closed interval outside the support of the limiting distribution, for sufficiently large n. The problem is motivated by applications in spatio-temporal statistics and …Cited by: 77

No eigenvalues outside the support of the limiting ...

    https://core.ac.uk/download/pdf/82374694.pdf
    results do not rule out the possibility of o.n/ eigenvalues scattered outside the support of the limiting empirical spectral distribution. The goal of our research is to establish that such a phenomenon does not occur for large enough n. Further research in our framework would allow for precise description of the location of the eigenvalues.

[PDF] No eigenvalues outside the support of the limiting ...

    https://www.semanticscholar.org/paper/No-eigenvalues-outside-the-support-of-the-limiting-Bai-Silverstein/dcfddb33ea6fa0dba831b2a51e87a64b7021a167
    In this paper we prove that, under certain conditions on the eigenvalues of T n , for any closed interval outside the support of the limit, with probability 1 there will be no eigenvalues …

[1801.03319] No eigenvalues outside the limiting support ...

    https://arxiv.org/abs/1801.03319
    We proved that under some mild assumptions, with probability 1, there will be no eigenvalues in any closed interval contained in an open interval outside the supports of the limiting distribution $F_{c_n,H_n}$, for all sufficiently large $n$. An extension of Bai-Yin law is also obtained.Cited by: 1

No Eigenvalues Outside the Support of the Limiting ...

    https://jack.math.ncsu.edu/noeigenvalues.pdf
    (1998) and Paul and Silverstein (2007), the nonexistence of eigenvalues outside the support of F. It is necessary at this point to review some of the properties of F and m F, obtained in Dozier and Silverstein (2007b). It is shown that for all x2R f 0g, lim z2C+!xm F(z) m 0(x) exists. From this it follows that Fhas a continuous derivative

No Eigenvalues Outside the Limiting Support of Generally ...

    https://repository.kaust.edu.sa/bitstream/handle/10754/610651/07464912.pdf?sequence=1&isAllowed=y
    under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this …

NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING ...

    https://www.worldscientific.com/doi/10.1142/S2010326311500043
    In this paper we show that, under certain conditions on R n, for any closed interval in ℝ + outside the support of the limiting distribution, then, almost surely, no eigenvalues of …Cited by: 25

Bai , Silverstein : No eigenvalues outside the support of ...

    https://projecteuclid.org/euclid.aop/1022855421
    No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Z. D. Bai and Jack W. Silverstein

No eigenvalues outside the support of the limiting ...

    https://www.sciencedirect.com/science/article/pii/S0047259X08001024
    We show that, under appropriate conditions on the eigenvalues of A n and B n, with probability 1, there will be no eigenvalues in any closed interval outside the support of the limiting distribution, for sufficiently large n. The problem is motivated by applications in spatio-temporal statistics and …Cited by: 77

No eigenvalues outside the support of the limiting ...

    https://core.ac.uk/download/pdf/82374694.pdf
    results do not rule out the possibility of o.n/ eigenvalues scattered outside the support of the limiting empirical spectral distribution. The goal of our research is to establish that such a phenomenon does not occur for large enough n. Further research in our framework would allow for precise description of the location of the eigenvalues.

[PDF] No eigenvalues outside the support of the limiting ...

    https://www.semanticscholar.org/paper/No-eigenvalues-outside-the-support-of-the-limiting-Bai-Silverstein/dcfddb33ea6fa0dba831b2a51e87a64b7021a167
    In this paper we prove that, under certain conditions on the eigenvalues of T n , for any closed interval outside the support of the limit, with probability 1 there will be no eigenvalues …

[1801.03319] No eigenvalues outside the limiting support ...

    https://arxiv.org/abs/1801.03319
    We gratefully acknowledge support from the Simons Foundation ... No eigenvalues outside the limiting support of the spectral distribution of general sample covariance matrices. ... We proved that under some mild assumptions, with probability 1, there will be no eigenvalues in any closed interval contained in an open interval outside the ...Cited by: 1

No eigenvalues outside the limiting support of the ...

    https://arxiv.org/pdf/1801.03319
    /No eigenvalues outside the support 5 Theorem 1.5. Under the abovemodel and assuming(a-e) with one more assumptions (f) The interval [a,b]with a > 0 lies outside the support of Fc n,H n for all large n, we have P no eigenvaluesof S n appears in [a,b] for all large n = 1. Remark 1.6. From the next section, one may find that also the strategy of the proof ofCited by: 1

No eigenvalues outside the support of limiting empirical ...

    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.149.6715&rep=rep1&type=pdf
    conditions on the eigenvalues of An and Bn, with probability 1, there will be no eigenvalues in any closed interval outside the support of the limiting distribution, for su–ciently large n. The problem is motivated by applications in spatio-temporal statistics and wireless communications.

Bai , Silverstein : No eigenvalues outside the support of ...

    https://projecteuclid.org/euclid.aop/1022855421
    Ann. Probab. Volume 26, Number 1 (1998), 316-345. No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices

No eigenvalues outside the support of limiting empirical ...

    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.149.6715&rep=rep1&type=pdf
    conditions on the eigenvalues of An and Bn, with probability 1, there will be no eigenvalues in any closed interval outside the support of the limiting distribution, for su–ciently large n. The problem is motivated by applications in spatio-temporal statistics and wireless communications.

NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING ...

    https://www.worldscientific.com/doi/10.1142/S2010326311500043
    In this paper we show that, under certain conditions on R n, for any closed interval in ℝ + outside the support of the limiting distribution, then, almost surely, no …Cited by: 25

No Eigenvalues Outside the Support of the Limiting ...

    https://jack.math.ncsu.edu/noeigenvalues.pdf
    No Eigenvalues Outside the Support of the Limiting Spectral Distribution of Information-Plus-Noise Type Matrices Zhidong Baiy1 and Jack W. Silversteinz2 yKLAS MOE & School of Mathematics and Statistics, Northeast Normal University,

No eigenvalues outside the support of the limiting ...

    https://www.sciencedirect.com/science/article/pii/S0047259X08001024
    We show that, under appropriate conditions on the eigenvalues of A n and B n, with probability 1, there will be no eigenvalues in any closed interval outside the support of the limiting distribution, for sufficiently large n. The problem is motivated by applications in spatio …Cited by: 77

No Eigenvalues Outside the Limiting Support of Generally ...

    https://repository.kaust.edu.sa/bitstream/handle/10754/610651/07464912.pdf?sequence=1&isAllowed=y
    eigenvalues of 1 n n in any closed interval outside the support of the limiting distribution. This result, often referred to as a no-eigenvalue result, has been established in [8] for the simple-correlated case where the columns of nare correlated with the same correlation matrix and …

No eigenvalues outside the limiting support of the ...

    https://arxiv.org/pdf/1801.03319
    /No eigenvalues outside the support 5 Theorem 1.5. Under the abovemodel and assuming(a-e) with one more assumptions (f) The interval [a,b]with a > 0 lies outside the support of Fc n,H n for all large n, we have P no eigenvaluesof SCited by: 1

[PDF] No eigenvalues outside the support of the limiting ...

    https://www.semanticscholar.org/paper/No-eigenvalues-outside-the-support-of-the-limiting-Bai-Silverstein/dcfddb33ea6fa0dba831b2a51e87a64b7021a167
    No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices @inproceedings{Bai1998NoEO, title={No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices}, author={Z. D. Bai and Jack W. Silverstein}, year={1998} }

Jack W. Silverstein

    https://jack.math.ncsu.edu/
    Jul 30, 2007 · No Eigenvalues Outside the Support of the Limiting Spectral Distribution of Information-Plus Noise Type Matrices.pdf file of my paper with Romain Couillet, Zhidong Bai, and Merouane Debbah. Eigen-inference for Energy Estimation of Multiple Sources. and the book Zhidong Bai and I have written: Spectral Analysis of Large Dimensional Random Matrices

(PDF) No Eigenvalues Outside the Support of the Limiting ...

    https://www.researchgate.net/publication/2580667_No_Eigenvalues_Outside_the_Support_of_the_Limiting_Spectral_Distribution_of_Large_Dimensional_Sample_Covariance_Matrices
    We prove that, under certain conditions on the eigenvalues of T n , for any closed interval outside the support of the limit, with probability 1 there will be no eigenvalues in this interval for ...

(PDF) No Eigenvalues Outside the Support of the Limiting ...

    https://www.researchgate.net/publication/2580667_No_Eigenvalues_Outside_the_Support_of_the_Limiting_Spectral_Distribution_of_Large_Dimensional_Sample_Covariance_Matrices
    We prove that, under certain conditions on the eigenvalues of T n , for any closed interval outside the support of the limit, with probability 1 there will be no eigenvalues in this interval for ...

No eigenvalues outside the support of the limiting ...

    https://core.ac.uk/download/pdf/82374694.pdf
    No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix Debashis Paula,, Jack W. Silversteinb,c a Department of Statistics, University of California, Davis, CA 95616, USA b Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA

[1801.03319] No eigenvalues outside the limiting support ...

    https://arxiv.org/abs/1801.03319
    We gratefully acknowledge support from the Simons Foundation ... No eigenvalues outside the limiting support of the spectral distribution of general sample covariance matrices. ... We proved that under some mild assumptions, with probability 1, there will be no eigenvalues in any closed interval contained in an open interval outside the ...

No eigenvalues outside the support of the limiting ...

    https://www.researchgate.net/publication/222828404_No_eigenvalues_outside_the_support_of_the_limiting_empirical_spectral_distribution_of_a_separable_covariance_matrix
    No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix Article in Journal of Multivariate Analysis 100(1):37-57 · January 2009 with 64 ...

CiteSeerX — No eigenvalues outside the support of the ...

    http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.9622
    In this paper we show that, under certain conditions on Rn, for any closed interval in R + outside the support of the limiting distribution, then, almost surely, no eigenvalues of …

Random Matrices in Wireless Communications Course 3 ...

    https://romaincouillet.hebfree.org/docs/courses/rmt/course_RMT_3.pdf
    No eigenvalues outside the support Absence of eigenvalues outside the support No eigenvalue outside the support of sample covariance matrices Z. D. Bai, J. W. Silverstein, “No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices,” The Annals of Probability, vol. 26, no.1 pp.

Convergence of the largest singular value of a polynomial ...

    https://experts.umn.edu/en/publications/convergence-of-the-largest-singular-value-of-a-polynomial-in-inde
    N2 - For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variables, under fourth moment hypotheses. We actually prove a more general result of the form "no eigenvalues outside the support of the limiting eigenvalue distribution."

Bai , Silverstein : CLT for linear spectral statistics of ...

    https://projecteuclid.org/euclid.aop/1078415845
    Project Euclid - mathematics and statistics online. No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices Bai, Z. D. and Silverstein, Jack W., The Annals of Probability, 1998

No Eigenvalues Outside the Limiting Support of Generally ...

    https://repository.kaust.edu.sa/handle/10754/610651
    Following the approach proposed in [1], we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero.

No eigenvalues outside the limiting support of the ...

    http://adsabs.harvard.edu/abs/2018arXiv180103319Y
    ADS Classic is now deprecated. It will be completely retired in October 2019. Please redirect your searches to the new ADS modern form or the classic form.More info can be found on our blog.

Crash Course on Random Matrix Theory Part II: Advanced ...

    https://romaincouillet.hebfree.org/docs/courses/rmt/crash_course_RMT_27_MORNING.pdf
    J. W. Silverstein, P. Debashis, \No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix," J. of Multivariate Analysis vol. 100, no. 1, pp. 37-57, 2009. I It has already been shown that (for all large N) there is no eigenvalues outside the support of

Support properties of spectra of polynomials in Wigner ...

    http://www-users.math.umn.edu/~gwanders/Postings/IMApresentationWRAP.pdf
    \No eigenvalues outside the support..." (Bai-Silverstein) A very important result on spectral support is due to Bai-Silverstein [Bai-Silverstein 1998]. It is the archetype for all the results to be discussed in this course but it is still not completely encompassed by the theory it has inspired.

CONVERGENCE OF THE LARGEST SINGULAR VALUE OF A …

    http://www-users.math.umn.edu/~gwanders/Postings/Filbert10.pdf
    earlier work of [9]) that there are for large Nalmost surely no eigenvalues outside an -neighborhood of the support of the limiting spectral distribution of a self-adjoint polynomial in independent GUE matrices. (See [1, Chap. 5, Sec. 5] for another account of that result.) It is natural to ask if the same is true for Wigner matrices.

Eigenvalue - an overview ScienceDirect Topics

    https://www.sciencedirect.com/topics/engineering/eigenvalue
    The system is small-signal stable as all the eigenvalues have negative real parts, but it is poorly damped due to many of its eigenvalues being outside the 10% damping conic section, especially those which have an absolute of the imaginary part less than 2π (that is, with frequencies less than 1 Hz).



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