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Volumn 143, Issue 3-4, 2009, Pages 481-516

Universality results for the largest eigenvalues of some sample covariance matrix ensembles

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EID: 59449098080     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0133-7     Document Type: Article
Times cited : (91)

References (38)
  • 1
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large-dimensional random matrices, a review
    • 3
    • Z.D. Bai 1999 Methodologies in spectral analysis of large-dimensional random matrices, a review Stat. Sin. 9 3 611 677
    • (1999) Stat. Sin. , vol.9 , pp. 611-677
    • Bai, Z.D.1
  • 2
    • 0001136512 scopus 로고
    • On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix
    • Z.D. Bai P.R. Krishnaiah Y.Q. Yin 1988 On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix Probab. Theor. Relat. Fields 78 509 521
    • (1988) Probab. Theor. Relat. Fields , vol.78 , pp. 509-521
    • Bai, Z.D.1    Krishnaiah, P.R.2    Yin, Y.Q.3
  • 3
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
    • 5
    • J. Baik G. Ben Arous S. Péché 2005 Phase transition of the largest eigenvalue for non-null complex sample covariance matrices Ann. Probab. 33 5 1643 1697
    • (2005) Ann. Probab. , vol.33 , pp. 1643-1697
    • Baik, J.1    Ben Arous, G.2    Péché, S.3
  • 4
    • 33646507506 scopus 로고    scopus 로고
    • Eigenvalues of large sample covariance matrices of spiked population models
    • J. Baik J. Silverstein 2006 Eigenvalues of large sample covariance matrices of spiked population models J. Mult. Anal. 97 1382 1408
    • (2006) J. Mult. Anal. , vol.97 , pp. 1382-1408
    • Baik, J.1    Silverstein, J.2
  • 5
    • 0000112246 scopus 로고
    • Exponential ensembles for random matrices
    • B.V. Bronk 1965 Exponential ensembles for random matrices J. Math. Phys. 6 228 237
    • (1965) J. Math. Phys. , vol.6 , pp. 228-237
    • Bronk, B.V.1
  • 7
    • 59449104004 scopus 로고    scopus 로고
    • On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity
    • El Karoui, N.: On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity. ArXiv math.ST/0309355 (2003)
    • (2003) ArXiv math.ST/0309355
    • El Karoui, N.1
  • 8
    • 33645016053 scopus 로고    scopus 로고
    • Recent results about the largest eigenvalue of random covariance matrices and statistical application
    • 9
    • N. El Karoui 2005 Recent results about the largest eigenvalue of random covariance matrices and statistical application Acta Phys. Polon. B 36 9 2681 2697
    • (2005) Acta Phys. Polon. B , vol.36 , pp. 2681-2697
    • El Karoui, N.1
  • 9
    • 59449093700 scopus 로고    scopus 로고
    • The largest eigenvalue of some rank one deformation of large Wigner matrices
    • Comm. Math. Phys. (to appear)
    • Féral, D., Péché, S.: The largest eigenvalue of some rank one deformation of large Wigner matrices. ArXiv math.PR/0605624. Comm. Math. Phys. (to appear) (2006)
    • (2006) ArXiv math.PR/0605624
    • Féral, D.1    Péché, S.2
  • 10
    • 0001436319 scopus 로고
    • A limit theorem for the norm of random matrices
    • S. Geman 1980 A limit theorem for the norm of random matrices Ann. Prob. 8 252 261
    • (1980) Ann. Prob. , vol.8 , pp. 252-261
    • Geman, S.1
  • 11
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • H. Hotelling 1933 Analysis of a complex of statistical variables into principal components J. Educ. Psychol. 24 417 441
    • (1933) J. Educ. Psychol. , vol.24 , pp. 417-441
    • Hotelling, H.1
  • 13
    • 0001154834 scopus 로고
    • Distributions of matrix variates and latent roots derived from normal samples
    • A. James 1960 Distributions of matrix variates and latent roots derived from normal samples Ann. Math. Stat. 31 151 158
    • (1960) Ann. Math. Stat. , vol.31 , pp. 151-158
    • James, A.1
  • 14
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • K. Johansson 2000 Shape fluctuations and random matrices Comm. Math. Phys. 209 437 476
    • (2000) Comm. Math. Phys. , vol.209 , pp. 437-476
    • Johansson, K.1
  • 15
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest principal component
    • I.M. Johnstone 2001 On the distribution of the largest principal component Ann. Stat. 29 295 327
    • (2001) Ann. Stat. , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 17
    • 0001967458 scopus 로고
    • Some limit theorems for the eigenvalues of sample covariance matrices
    • D. Jonsson 1982 Some limit theorems for the eigenvalues of sample covariance matrices J. Mult. Anal. 12 1 38
    • (1982) J. Mult. Anal. , vol.12 , pp. 1-38
    • Jonsson, D.1
  • 19
    • 0242522220 scopus 로고    scopus 로고
    • Collective origin of the coexisence of apparent RMT noise and factors in large sample correlation matrices
    • 3-4
    • Y. Malevergne D. Sornette 2004 Collective origin of the coexisence of apparent RMT noise and factors in large sample correlation matrices Physica A 331 3-4 660 668
    • (2004) Physica A , vol.331 , pp. 660-668
    • Malevergne, Y.1    Sornette, D.2
  • 20
    • 0000263234 scopus 로고
    • Distribution of eigenvalues forsome sets of random matrices
    • V.A. Marcenko L.A. Pastur 1967 Distribution of eigenvalues forsome sets of random matrices Math. USSR-Sbornik 1 457 486
    • (1967) Math. USSR-Sbornik , vol.1 , pp. 457-486
    • Marcenko, V.A.1    Pastur, L.A.2
  • 21
    • 33846006923 scopus 로고    scopus 로고
    • Population structure and eigenanalysis
    • DOI:
    • Patterson, N., Price, A.L., Reich, D.: Population structure and eigenanalysis. PLoS Genet 2(12), e190 (2006) DOI: 10.1371/journal.pgen.0020190
    • (2006) PLoS Genet , vol.2 , Issue.12 , pp. 190
    • Patterson, N.1    Price, A.L.2    Reich, D.3
  • 22
    • 36448958660 scopus 로고    scopus 로고
    • Wigner random matrices with non-symmetrically distributed entries
    • arXiv:math/0702035. Applications of random matrices, determinants and pfaffians to problems in statistical mechanics to appear
    • Péché, S., Soshnikov, A.: Wigner random matrices with non-symmetrically distributed entries. arXiv:math/0702035. Applications of random matrices, determinants and pfaffians to problems in statistical mechanics. J. Stat. Phys (to appear) (2007)
    • (2007) J. Stat. Phys
    • Péché, S.1    Soshnikov, A.2
  • 23
    • 0039659644 scopus 로고    scopus 로고
    • On the eigenvalue distribution of some symmetric random matrices
    • F. Oravecz D. Petz 1997 On the eigenvalue distribution of some symmetric random matrices Acta Sci. Math. 63 383 395
    • (1997) Acta Sci. Math. , vol.63 , pp. 383-395
    • Oravecz, F.1    Petz, D.2
  • 25
    • 28144459476 scopus 로고    scopus 로고
    • Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries
    • A. Ruzmaikina 2006 Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries Commun. Math. Phys. 261 277 296
    • (2006) Commun. Math. Phys. , vol.261 , pp. 277-296
    • Ruzmaikina, A.1
  • 26
    • 0942290020 scopus 로고    scopus 로고
    • Instabilities in complex mixtures with a large number of components
    • 24
    • R. Sear J. Cuesta 2003 Instabilities in complex mixtures with a large number of components Phys. Rev. Lett. 91 24 245 701
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 245-701
    • Sear, R.1    Cuesta, J.2
  • 27
    • 0141730574 scopus 로고
    • On the weak limit of the largest eigenvalue of a large-dimensional sample covariance matrix
    • 2
    • J. Silverstein 1989 On the weak limit of the largest eigenvalue of a large-dimensional sample covariance matrix J. Multivariate Anal. 30 2 307 311
    • (1989) J. Multivariate Anal. , vol.30 , pp. 307-311
    • Silverstein, J.1
  • 28
    • 27144550468 scopus 로고    scopus 로고
    • Central limit theorem for traces of large random symmetric matrices with independent matrix elements
    • 1
    • Y. Sinai A. Soshnikov 1998 Central limit theorem for traces of large random symmetric matrices with independent matrix elements Bol. Soc. Brasil. Mat. (N.S.) 29 1 1 24
    • (1998) Bol. Soc. Brasil. Mat. (N.S.) , vol.29 , pp. 1-24
    • Sinai, Y.1    Soshnikov, A.2
  • 29
    • 0343861172 scopus 로고    scopus 로고
    • A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices
    • Y. Sinai A. Soshnikov 1998 A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices Funct. Anal. Appl. 32 114 131
    • (1998) Funct. Anal. Appl. , vol.32 , pp. 114-131
    • Sinai, Y.1    Soshnikov, A.2
  • 30
    • 0033473406 scopus 로고    scopus 로고
    • Universality at the edge of the spectrum in Wigner random matrices
    • A. Soshnikov 1999 Universality at the edge of the spectrum in Wigner random matrices Commun. Math. Phys. 207 697 733
    • (1999) Commun. Math. Phys. , vol.207 , pp. 697-733
    • Soshnikov, A.1
  • 31
    • 0141450345 scopus 로고    scopus 로고
    • A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
    • A. Soshnikov 2002 A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices J. Stat. Phys. 108 1033 1056
    • (2002) J. Stat. Phys. , vol.108 , pp. 1033-1056
    • Soshnikov, A.1
  • 33
    • 0041962802 scopus 로고    scopus 로고
    • Counting lattice paths by Narayana polynomials
    • electronic
    • Sulanke, R.: Counting lattice paths by Narayana polynomials. Electron. J. Combin. 7, 9p (electronic) (2000)
    • (2000) Electron. J. Combin. , vol.7 , pp. 9
    • Sulanke, R.1
  • 35
    • 0004083131 scopus 로고    scopus 로고
    • Capacity of multi-antenna Gaussian channels
    • 6
    • E. Telatar 1999 Capacity of multi-antenna Gaussian channels Eur. Trans. Telecomm. 10 6 585 595
    • (1999) Eur. Trans. Telecomm. , vol.10 , pp. 585-595
    • Telatar, E.1
  • 36
    • 27644532196 scopus 로고
    • Level-spacing distribution and Airy kernel
    • C. Tracy H. Widom 1994 Level-spacing distribution and Airy kernel Commun. Math. Phys. 159 151 174
    • (1994) Commun. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 37
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • C. Tracy H. Widom 1996 On orthogonal and symplectic matrix ensembles Commun. Math. Phys. 177 727 754
    • (1996) Commun. Math. Phys. , vol.177 , pp. 727-754
    • Tracy, C.1    Widom, H.2
  • 38
    • 0002247902 scopus 로고
    • The strong limits of random matrix spectra for sample covariance matrices of independent elements
    • K. Wachter 1978 The strong limits of random matrix spectra for sample covariance matrices of independent elements Ann. Probab. 6 1 18
    • (1978) Ann. Probab. , vol.6 , pp. 1-18
    • Wachter, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.