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Volumn 38, Issue 5, 2010, Pages 2023-2065

Random matrices: Universality of ESDs and the circular law

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EID: 77957124985     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOP534     Document Type: Article
Times cited : (392)

References (27)
  • 1
    • 0031534271 scopus 로고    scopus 로고
    • Circular law
    • BAI, Z. D. (1997). Circular law. Ann. Probab. 25 494-529.
    • (1997) Ann. Probab. , vol.25 , pp. 494-529
    • Bai, Z.D.1
  • 3
    • 33846999295 scopus 로고    scopus 로고
    • On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices
    • DOZIER, R. B. and SILVERSTEIN, J. W. (2007). On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices. J. Multivariate Anal. 98 678-694.
    • (2007) J. Multivariate Anal. , vol.98 , pp. 678-694
    • Dozier, R.B.1    Silverstein, J.W.2
  • 6
    • 0000324960 scopus 로고
    • Eigenvalues and condition numbers of random matrices
    • EDELMAN, A. (1988). Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Appl. 9 543-560.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 543-560
    • Edelman, A.1
  • 7
    • 0001393752 scopus 로고
    • The circular law
    • GIRKO, V. L. (1984). The circular law. Theory Probab. Appl. 29 694-706.
    • (1984) Theory Probab. Appl. , vol.29 , pp. 694-706
    • Girko, V.L.1
  • 8
    • 44249096503 scopus 로고    scopus 로고
    • The strong circular law. Twenty years later. II
    • GIRKO, V. L. (2004). The strong circular law. Twenty years later. II. Random Oper. Stochastic Equations 12 255-312.
    • (2004) Random Oper. Stochastic Equations , vol.12 , pp. 255-312
    • Girko, V.L.1
  • 12
    • 0012942540 scopus 로고    scopus 로고
    • The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs
    • Providence, RI
    • LEDOUX, M. (2001). The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs 89. Amer. Math. Soc., Providence, RI.
    • (2001) Amer. Math. Soc. , vol.89
    • Ledoux, M.1
  • 14
    • 72549096261 scopus 로고    scopus 로고
    • Circular law, extreme singular values and potential theory
    • PAN, G. and ZHOU, W. (2010). Circular law, extreme singular values and potential theory. J. Multivariate Anal. 101 645-656.
    • (2010) J. Multivariate Anal. , vol.101 , pp. 645-656
    • Pan, G.1    Zhou, W.2
  • 15
    • 0002728031 scopus 로고
    • The spectrum of random matrices
    • PASTUR, L. A. (1972). The spectrum of random matrices. Teoret. Mat. Fiz. 10 102-112.
    • (1972) Teoret. Mat. Fiz. , vol.10 , pp. 102-112
    • Pastur, L.A.1
  • 16
    • 49649108303 scopus 로고    scopus 로고
    • Invertibility of random matrices: Norm of the inverse
    • RUDELSON, M. (2008). Invertibility of random matrices: Norm of the inverse. Ann. of Math. (2) 168 575-600.
    • (2008) Ann. of Math. , vol.168 , Issue.2 , pp. 575-600
    • Rudelson, M.1
  • 18
    • 76749128899 scopus 로고    scopus 로고
    • Smallest singular value of a random rectangular matrix
    • RUDELSON, M. and VERSHYNIN, R. (2009). Smallest singular value of a random rectangular matrix. Comm. Pure Appl. Math. 62 1707-1739.
    • (2009) Comm. Pure Appl. Math. , vol.62 , pp. 1707-1739
    • Rudelson, M.1    Vershynin, R.2
  • 19
    • 41049114969 scopus 로고    scopus 로고
    • The Littlewood-Offord problem and the condition number of random matrices
    • RUDELSON, M. and VERSHYNIN, R. (2010). The Littlewood-Offord problem and the condition number of random matrices. Adv. Math. 218 600-633.
    • (2010) Adv. Math. , vol.218 , pp. 600-633
    • Rudelson, M.1    Vershynin, R.2
  • 21
    • 33645288547 scopus 로고    scopus 로고
    • On random ±1 matrices: Singularity and determinant
    • TAO, T. and VU, V. (2006). On random ±1 matrices: Singularity and determinant. Random Structures Algorithms 28 1-23.
    • (2006) Random Structures Algorithms , vol.28 , pp. 1-23
    • Tao, T.1    Vu, V.2
  • 22
  • 23
    • 71849089047 scopus 로고    scopus 로고
    • Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
    • TAO, T. and VU, V. H. (2009). Inverse Littlewood-Offord theorems and the condition number of random discrete matrices. Ann. of Math. (2) 169 595-632.
    • (2009) Ann. of Math. , vol.169 , Issue.2 , pp. 595-632
    • Tao, T.1    Vu, V.H.2
  • 25
    • 44249125025 scopus 로고    scopus 로고
    • Random matrices: The circular law
    • TAO, T. and VU, V. (2008). Random matrices: The circular law. Commun. Contemp. Math. 10 261-307.
    • (2008) Commun. Contemp. Math. , vol.10 , pp. 261-307
    • Tao, T.1    Vu, V.2
  • 26
    • 77952883804 scopus 로고    scopus 로고
    • Random matrices: The distribution of the smallest singular values
    • TAO, T. and VU, V. (2010). Random matrices: The distribution of the smallest singular values. Geom. Funct. Anal. 20 260-297.
    • (2010) Geom. Funct. Anal. , vol.20 , pp. 260-297
    • Tao, T.1    Vu, V.2
  • 27
    • 0001560594 scopus 로고
    • On the distribution of the roots of certain symmetric matrices
    • WIGNER, E. P. (1958). On the distribution of the roots of certain symmetric matrices. Ann. of Math. (2) 67 325-327.
    • (1958) Ann. of Math. , vol.67 , Issue.2 , pp. 325-327
    • Wigner, E.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.