메뉴 건너뛰기




Volumn 2, Issue 1, 2013, Pages

On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations

Author keywords

outliers; Random matrices

Indexed keywords


EID: 84906824429     PISSN: 20103263     EISSN: 20103271     Source Type: Journal    
DOI: 10.1142/S2010326312500153     Document Type: Article
Times cited : (33)

References (50)
  • 2
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large-dimensional random matrices, a review
    • Z. D. Bai, Methodologies in spectral analysis of large-dimensional random matrices, a review, Statist. Sinica 9 (1999) 611-677.
    • (1999) Statist Sinica , vol.9 , pp. 611-677
    • Bai, Z.D.1
  • 3
    • 84855864044 scopus 로고    scopus 로고
    • Limiting behavior of eigenvectors of large Wigner matrices
    • Z. D. Bai and G. M. Pan, Limiting behavior of eigenvectors of large Wigner matrices, J. Statist. Phys. 146(3) (2012) 519-549.
    • (2012) J Statist. Phys. , vol.146 , Issue.3 , pp. 519-549
    • Bai, Z.D.1    Pan, G.M.2
  • 4
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
    • J. Baik, G. Ben Arous and S. Péché, Phase transition of the largest eigenvalue for non-null complex sample covariance matrices, Ann. Probab. 33 (2005) 1643-1697.
    • (2005) Ann. Probab. , vol.33 , pp. 1643-1697
    • Baik, J.1    Ben Arous, G.2    Péché, S.3
  • 5
    • 33646507506 scopus 로고    scopus 로고
    • Eigenvalues of large sample covariance matrices of spiked population models
    • J. Baik and J. W. Silverstein, Eigenvalues of large sample covariance matrices of spiked population models, J. Multi. Anal. 97 (2006) 1382-1408.
    • (2006) J. Multi. Anal. , vol.97 , pp. 1382-1408
    • Baik, J.1    Silverstein, J.W.2
  • 6
    • 84855867843 scopus 로고    scopus 로고
    • On the largest eigenvalue of a Hermitian random matrix model with spiked external source I
    • preprint
    • J. Baik and D. Wang, On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case, preprint (2010); http://arxiv.org/1010.4604.
    • (2010) Rank One Case
    • Baik, J.1    Wang, D.2
  • 7
    • 84855880530 scopus 로고    scopus 로고
    • On the largest eigenvalue of a Hermitian random matrix model with spiked external source II
    • preprint
    • J. Baik and D. Wang, On the largest eigenvalue of a Hermitian random matrix model with spiked external source II. Higher rank case, preprint (2011); http://arxiv.org//1104.2915.
    • (2011) Higher Rank Case
    • Baik, J.1    Wang, D.2
  • 8
    • 84919673367 scopus 로고    scopus 로고
    • Wigner matrices
    • eds. G. Akemann, J. Baik and P. Di Francesco (Oxford University Press, New York
    • G. Ben Arous and A. Guionnet, Wigner matrices, in Oxford Handbook on Random Matrix Theory, eds. G. Akemann, J. Baik and P. Di Francesco (Oxford University Press, New York, 2011).
    • (2011) Oxford Handbook on Random Matrix Theory
    • Ben Arous, G.1    Guionnet, A.2
  • 9
    • 80053163500 scopus 로고    scopus 로고
    • Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
    • F. Benaych-Georges, A. Guionnet and M. Maida, Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Electron. J. Probab. 16 (2011) 1621-1662.
    • (2011) Electron. J. Probab. , vol.16 , pp. 1621-1662
    • Benaych-Georges, F.1    Guionnet, A.2    Maida, M.3
  • 10
    • 84870540474 scopus 로고    scopus 로고
    • Large deviations of the extreme eigenvalues of random deformations of matrices
    • F. Benaych-Georges, A. Guionnet and M. Maida, Large deviations of the extreme eigenvalues of random deformations of matrices, Probab. Theory Related Fields 154(3-4) (2012) 703-751.
    • (2012) Probab. Theory Related Fields , vol.154 , Issue.3-4 , pp. 703-751
    • Benaych-Georges, F.1    Guionnet, A.2    Maida, M.3
  • 11
    • 79952708259 scopus 로고    scopus 로고
    • The eigenvalues and eigenvectors of finite low rank perturbations of large random matrices
    • F. Benaych-Georges and R. Rao, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices, Adv. Math. 227(1) (2011) 494-521.
    • (2011) Adv Math. , vol.227 , Issue.1 , pp. 494-521
    • Benaych-Georges, F.1    Rao, R.2
  • 15
    • 63049133332 scopus 로고    scopus 로고
    • The largest eigenvalue of finite rank deformation of large Wigner matrices: Convergence and non universality of the fluctuations
    • M. Capitaine, C. Donati-Martin and D. Féral, The largest eigenvalue of finite rank deformation of large Wigner matrices: Convergence and non universality of the fluctuations, Ann. Probab. 37 (2009) 1-47.
    • (2009) Ann. Probab. , vol.37 , pp. 1-47
    • Capitaine, M.1    Donati-Martin, C.2    Féral, D.3
  • 16
    • 84856279561 scopus 로고    scopus 로고
    • Central limit theorems for eigenvalues of deformations of Wigner matrices
    • M. Capitaine, C. Donati-Martin and D. Féral, Central limit theorems for eigenvalues of deformations of Wigner matrices, Ann. 48(1) (2012) 107-133.
    • (2012) Ann. , vol.48 , Issue.1 , pp. 107-133
    • Capitaine, M.1    Donati-Martin, C.2    Féral, D.3
  • 17
    • 80755159232 scopus 로고    scopus 로고
    • Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices
    • M. Capitaine, C. Donati-Martin, D. Féral and M. Février, Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices, Electron. J. Probab. 16(64) (2011) 1750-1792.
    • (2011) Electron. J. Probab. , vol.16 , Issue.64 , pp. 1750-1792
    • Capitaine, M.1    Donati-Martin, C.2    Féral, D.3    Février, M.4
  • 18
    • 0000787440 scopus 로고
    • The functional calculus
    • E. B. Davies, The functional calculus, J. London Math. Soc. 52 (1995) 166-176.
    • (1995) J. London Math. Soc. , vol.52 , pp. 166-176
    • Davies, E.B.1
  • 19
    • 80054099942 scopus 로고    scopus 로고
    • Universality of Wigner random matrices: A survey of recent results
    • L. Erdös, Universality ofWigner random matrices: A survey of recent results, Uspekhi Mat. Nauk 66 (2011) 67-198.
    • (2011) Uspekhi Mat. Nauk , vol.66 , pp. 67-198
    • Erdös, L.1
  • 21
    • 34248227713 scopus 로고    scopus 로고
    • The largest eigenvalue of rank one deformation of large Wigner matrices
    • D. Féral and S. Péché, The largest eigenvalue of rank one deformation of large Wigner matrices, Comm. Math. Phys. 272(1) (2007) 185-228.
    • (2007) Comm. Math. Phys. , vol.272 , Issue.1 , pp. 185-228
    • Féral, D.1    Péché, S.2
  • 22
    • 51249182622 scopus 로고
    • The eigenvalues of random symmetric matrices
    • Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices, Combinatorica 1 (1981) 233-241.
    • (1981) Combinatorica , vol.1 , pp. 233-241
    • Füredi, Z.1    Komlós, J.2
  • 24
    • 0000301201 scopus 로고
    • Equation de Schrödinger avec champ magnetique et equation de Harper
    • eds. H. Holden and A. Jensen Springer, Berlin
    • B. Helffer and J. Sjöstrand, Equation de Schrödinger avec champ magnetique et equation de Harper, in Schrödinger Operators, Lecture Notes in Physics, Vol. 345 eds. H. Holden and A. Jensen (Springer, Berlin, 1989), pp. 118-197.
    • (1989) Schrödinger Operators, Lecture Notes in Physics , vol.345 , pp. 118-197
    • Helffer, B.1    Sjöstrand, J.2
  • 25
    • 84856276225 scopus 로고    scopus 로고
    • Universality for certain Hermitian Wigner matrices under weak moment conditions
    • K. Johansson, Universality for certain Hermitian Wigner matrices under weak moment conditions, Ann. Inst. H. Doincaré Probab. Statist. 48(1) (2012) 47-79.
    • (2012) Ann. Inst. H. Doincaré Probab. Statist. , vol.48 , Issue.1 , pp. 47-79
    • Johansson, K.1
  • 26
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29 (2001) 295-327.
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 27
    • 0030494613 scopus 로고    scopus 로고
    • Asymptotic properties of large random matrices with independent entries
    • A. Khorunzhy, B. Khoruzhenko and L. Pastur, Asymptotic properties of large random matrices with independent entries, J. Math. Phys. 37 (1996) 5033-5060.
    • (1996) J. Math. Phys. , vol.37 , pp. 5033-5060
    • Khorunzhy, A.1    Khoruzhenko, B.2    Pastur, L.3
  • 32
    • 58549092109 scopus 로고    scopus 로고
    • Fluctuations of matrix elements of regular functions of Gaussian random matrices
    • A. Lytova and L. Pastur, Fluctuations of matrix elements of regular functions of Gaussian random matrices, J. Statist. Phys. 134 (2009) 147-159.
    • (2009) J. Statist. Phys. , vol.134 , pp. 147-159
    • Lytova, A.1    Pastur, L.2
  • 34
    • 34548315757 scopus 로고    scopus 로고
    • Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
    • M. Maida, Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles, Electron. J. Probab. 12 (2007) 1131-1150.
    • (2007) Electron. J. Probab. , vol.12 , pp. 1131-1150
    • Maida, M.1
  • 36
    • 84879219252 scopus 로고    scopus 로고
    • On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries
    • to appear
    • S. O'Rourke, D. Renfrew and A. Soshnikov, On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, to appear in J. Theoret. Probab.
    • J. Theoret. Probab
    • O'Rourke, S.1    Renfrew, D.2    Soshnikov, A.3
  • 37
    • 38549175880 scopus 로고    scopus 로고
    • Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
    • D. Paul, Asymptotics of sample eigenstructure for a large dimensional spiked covariance model, Statist. Sinica 17(4) (2007) 1617-1642.
    • (2007) Statist. Sinica , vol.17 , Issue.4 , pp. 1617-1642
    • Paul, D.1
  • 38
    • 28144463102 scopus 로고    scopus 로고
    • The largest eigenvalue of small rank perturbations of Hermitian random matrices
    • S. Péché, The largest eigenvalue of small rank perturbations of Hermitian random matrices, Probab. Theory Related Fields 134(1) (2006) 127-173.
    • (2006) Probab. Theory Related Fields , vol.134 , Issue.1 , pp. 127-173
    • Péché, S.1
  • 40
    • 84855885363 scopus 로고    scopus 로고
    • Fluctuations of matrix entries of regular functions of Wigner matrices
    • A. Pizzo, D. Renfrew and A. Soshnikov, Fluctuations of matrix entries of regular functions of Wigner matrices, J. Statist. Phys. 146(3) (2012) 550-591.
    • (2012) J. Statist. Phys. , vol.146 , Issue.3 , pp. 550-591
    • Pizzo, A.1    Renfrew, D.2    Soshnikov, A.3
  • 41
    • 84860437102 scopus 로고    scopus 로고
    • Central limit theorem for linear eigenvalue statistics of Wigner and sample covariance random matrices
    • M. Shcherbina, Central limit theorem for linear eigenvalue statistics of Wigner and sample covariance random matrices, J. Math. Phys. Anal. Geome. 7(2) (2011) 176-192.
    • (2011) J. Math. Phys. Anal. Geome. , vol.7 , Issue.2 , pp. 176-192
    • Shcherbina, M.1
  • 43
    • 85081395630 scopus 로고    scopus 로고
    • Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs
    • preprint
    • M. Shcherbina and B. Tirozzi, Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime, preprint (2011); arXiv.1111.5492.
    • (2011) Diluted Regime
    • Shcherbina, M.1    Tirozzi, B.2
  • 44
    • 0033473406 scopus 로고    scopus 로고
    • Universality at the edge of the spectrum in Wigner random matrices
    • A. Soshnikov, Universality at the edge of the spectrum in Wigner random matrices, Commun. Math. Phys. 207 (1999) 697-733.
    • (1999) Commun. Math. Phys. , vol.207 , pp. 697-733
    • Soshnikov, A.1
  • 45
    • 84941460976 scopus 로고
    • Bedingt konvergente Reihen und konvexe Systeme
    • E. Steinitz, Bedingt konvergente Reihen und konvexe Systeme, J. Reine Angew. Math. 143 (1913) 128-175.
    • (1913) J. Reine Angew. Math. , vol.143 , pp. 128-175
    • Steinitz, E.1
  • 46
    • 84872653524 scopus 로고    scopus 로고
    • Outliers in the spectrum of iid matrices with bounded rank perturbations
    • T. Tao, Outliers in the spectrum of iid matrices with bounded rank perturbations, Probab. Theory Related Fields. 155(1-2) (2013) 231-263.
    • (2013) Probab. Theory Related Fields. , vol.155 , Issue.1-2 , pp. 231-263
    • Tao, T.1
  • 47
    • 77954624704 scopus 로고    scopus 로고
    • Random matrices: Universality of local eigenvalue statistics up to the edge
    • T. Tao and V. Vu, Random matrices: Universality of local eigenvalue statistics up to the edge, Commun. Math. Phys. 298 (2010) 549-572.
    • (2010) Commun. Math. Phys. , vol.298 , pp. 549-572
    • Tao, T.1    Vu, V.2
  • 49
    • 27644532196 scopus 로고
    • Level spacing distributions and the Airy kernel
    • C. Tracy and H. Widom, Level spacing distributions and the Airy kernel, Commun. Math. Phys. 159 (1994) 151-174.
    • (1994) Commun. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 50
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • C. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996) 727-754.
    • (1996) Commun. Math. Phys. , vol.177 , pp. 727-754
    • Tracy, C.1    Widom, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.