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Volumn 118, Issue 2, 2002, Pages 290-304

Strong approximation of Eigenvalues of large dimensional Wishart matrices by roots of generalized laguerre polynomials

Author keywords

Laguerre polynomials; Mar enko Pastur law; Random matrix theory; Roots of orthogonal polynomials; Semicircle law; Strong approximation

Indexed keywords


EID: 0036808716     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.2002.3725     Document Type: Article
Times cited : (12)

References (17)
  • 1
    • 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
  • 2
    • 0011324907 scopus 로고
    • Convergence to the semicircle law
    • Z. D. Bai and Y. Q. Yin, Convergence to the semicircle law, Ann. Probab. 16 (1988), 863-875.
    • (1988) Ann. Probab , vol.16 , pp. 863-875
    • Bai, Z.D.1    Yin, Y.Q.2
  • 3
    • 0003007394 scopus 로고
    • Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix
    • Z. D. Bai and Y. Q. Yin, Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix, Ann. Probab. 16 (1988), 1729-1741.
    • (1988) Ann. Probab , vol.16 , pp. 1729-1741
    • Bai, Z.D.1    Yin, Y.Q.2
  • 4
    • 0001758959 scopus 로고
    • Limit of the smallest eigenvalue of a large dimensional covariance matrix
    • Z. D. Bai and Y. Q. Yin, Limit of the smallest eigenvalue of a large dimensional covariance matrix, Ann. Probab. 21 (1993), 1275-1294.
    • (1993) Ann. Probab , vol.21 , pp. 1275-1294
    • Bai, Z.D.1    Yin, Y.Q.2
  • 5
    • 0032207908 scopus 로고    scopus 로고
    • Strong asymptotics for Laguerre polynomials with varying weights
    • C. Bosbach and W. Gawronski, Strong asymptotics for Laguerre polynomials with varying weights, J. Comput. Appl. Math. 99 (1998), 77-89.
    • (1998) J. Comput. Appl. Math , vol.99 , pp. 77-89
    • Bosbach, C.1    Gawronski, W.2
  • 6
    • 0004165067 scopus 로고
    • "An Introduction to Orthogonal Polynomials"
    • Gordon and Breach, London
    • T. Chihara, "An Introduction to Orthogonal Polynomials," Gordon and Breach, London, 1978.
    • (1978)
    • Chihara, T.1
  • 7
    • 21844504037 scopus 로고
    • Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials
    • H. Dette and W. J. Studden, Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials, Constr. Approx. 11 (1995), 227-238.
    • (1995) Constr. Approx , vol.11 , pp. 227-238
    • Dette, H.1    Studden, W.J.2
  • 8
    • 0000084804 scopus 로고
    • Recurrence moment formulas for D-optimal designs
    • H. Dette and W. K. Wong, Recurrence moment formulas for D-optimal designs, Scand. J. Statist. 22 (1995), 505-512.
    • (1995) Scand. J. Statist , vol.22 , pp. 505-512
    • Dette, H.1    Wong, W.K.2
  • 9
    • 0001684607 scopus 로고
    • On the limit distribution of the zeros of Jonquiere polynomials and generalized classical orthogonal polynomials
    • J. Faldey and W. Gawronski, On the limit distribution of the zeros of Jonquiere polynomials and generalized classical orthogonal polynomials, J. Approx. Theory 81 (1995), 231-249.
    • (1995) J. Approx. Theory , vol.81 , pp. 231-249
    • Faldey, J.1    Gawronski, W.2
  • 11
    • 0001197443 scopus 로고
    • Über die Abgrenzung der Eigenwerte einer Matrix
    • S. A. Geršgorin, Über die Abgrenzung der Eigenwerte einer Matrix, Ivz. Akad. Nauk. SSSR Ser. Fiz.-Mat. 6 (1931), 749-754.
    • (1931) Ivz. Akad. Nauk. SSSR Ser. Fiz.-Mat , vol.6 , pp. 749-754
    • Geršgorin, S.A.1
  • 12
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest principal component
    • I. M. Johnstone, On the distribution of the largest principal component, Ann. Statist., 29 (2001), 295-327.
    • (2001) Ann. Statist , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 13
    • 0001114597 scopus 로고    scopus 로고
    • The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
    • A. B. J. Kuijlaars and W. Van Assche, The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients, J. Approx. Theory 99 (1999), 167-197.
    • (1999) J. Approx. Theory , vol.99 , pp. 167-197
    • Kuijlaars, A.B.J.1    Van Assche, W.2
  • 14
    • 0000263239 scopus 로고
    • Distributions of eigenvalues of some sets of random matrices
    • V. A. Marčenko and L. A. Pastur, Distributions of eigenvalues of some sets of random matrices, Math. USSR-Sb. 1 (1967), 507-536.
    • (1967) Math. USSR-Sb , vol.1 , pp. 507-536
    • Marčenko, V.A.1    Pastur, L.A.2
  • 15
    • 0001629248 scopus 로고
    • The smallest eigenvalue of a large dimensional Wishart matrix
    • J. Silverstein, The smallest eigenvalue of a large dimensional Wishart matrix, Ann. Probab. 13 (1985), 1364-1368.
    • (1985) Ann. Probab , vol.13 , pp. 1364-1368
    • Silverstein, J.1
  • 16
    • 0003362643 scopus 로고
    • "Orthogonal Polynomials"
    • Providence, RI
    • G. Szegö, "Orthogonal Polynomials," Amer. Math. Soc., Providence, RI, 1959.
    • (1959) Amer. Math. Soc
    • Szegö, G.1
  • 17
    • 0000840166 scopus 로고
    • On the distribution of the roots of certain symmetric matrices
    • E. P. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. Math. 62 (1955), 548-564.
    • (1955) Ann. Math , vol.62 , pp. 548-564
    • Wigner, E.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.