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Volumn 22, Issue 3, 2012, Pages 1266-1300

Universality and the circular law for sparse random matrices

Author keywords

Circular law; Random matrix; Sparse matrix

Indexed keywords


EID: 84879635482     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AAP789     Document Type: Article
Times cited : (60)

References (36)
  • 2
    • 0031534271 scopus 로고    scopus 로고
    • Circular law
    • MR1428519
    • BAI, Z. D. (1997). Circular law. Ann. Probab. 25 494-529. MR1428519
    • (1997) Ann. Probab. , vol.25 , pp. 494-529
    • Bai, Z.D.1
  • 7
    • 33846999295 scopus 로고    scopus 로고
    • On the empirical distribution ofeigenvalues oflarge dimensional information-plus-noise-type matrices
    • MR2322123
    • DOZIER, R. B. and SILVERSTEIN, J. W. (2007). On the empirical distribution ofeigenvalues oflarge dimensional information-plus-noise-type matrices. J. Multivariate Anal. 98 678-694. MR2322123
    • (2007) J. Multivariate Anal. , vol.98 , pp. 678-694
    • Dozier, R.B.1    Silverstein, J.W.2
  • 9
    • 33744857123 scopus 로고    scopus 로고
    • Statistical properties of sparse Gaussian random symmetrical ensemble
    • MR1456787
    • DURAS, M. M., SOKALSKI, K. and SUłKOWSKI, P. (1997). Statistical properties of sparse Gaussian random symmetrical ensemble. Acta Phys. Polon. B 28 1023-1038. MR1456787
    • (1997) Acta Phys. Polon. B , vol.28 , pp. 1023-1038
    • Duras, M.M.1    Sokalski, K.2    Sułkowski, P.3
  • 11
    • 0000324960 scopus 로고
    • Eigenvalues and condition numbers ofrandommatrices
    • MR0964668
    • EDELMAN, A. (1988). Eigenvalues and condition numbers ofrandommatrices. SIAMJ. Matrix Anal. Appl. 9 543-560. MR0964668
    • (1988) SIAMJ. Matrix Anal. Appl. , vol.9 , pp. 543-560
    • Edelman, A.1
  • 12
    • 0000802722 scopus 로고    scopus 로고
    • Universality in the random matrix spectra in the regime of weak non-Hermiticity: Classical and quantum chaos
    • MR1634312
    • FYODOROV, Y. V., SOMMERS, H.-J. and KHORUZHENKO, B. A. (1998). Universality in the random matrix spectra in the regime of weak non-Hermiticity: Classical and quantum chaos. Ann. Inst. H. Poincaré Phys. Théor. 68 449-489. MR1634312
    • (1998) Ann. Inst. H. Poincaré. Phys. Théor. , vol.68 , pp. 449-489
    • Fyodorov, Y.V.1    Sommers, H.-J.2    Khoruzhenko, B.A.3
  • 13
    • 0039799159 scopus 로고
    • The circular law
    • MR0773436
    • GIRKO, V. L. (1984). The circular law. Teor. Veroyatn. Primen. 29 669-679. MR0773436
    • (1984) Teor. Veroyatn. Primen. , vol.29 , pp. 669-679
    • Girko, V.L.1
  • 14
    • 44249096503 scopus 로고    scopus 로고
    • The strong circular law. Twenty years later. II. Random
    • MR2085255
    • GIRKO, V. L. (2004). The strong circular law. Twenty years later. II. Random Oper. Stoch. Equ. 12 255-312. MR2085255
    • (2004) Oper. Stoch. Equ. , Issue.12 , pp. 255-312
    • Girko, V.L.1
  • 16
    • 77957039680 scopus 로고    scopus 로고
    • The circular law for random matrices
    • MR2663633
    • GÖTZE, F. and TIKHOMIROV, A. (2010). The circular law for random matrices. Ann. Probab. 38 1444-1491. MR2663633
    • (2010) Ann. Probab. , vol.38 , pp. 1444-1491
    • Götze, F.1    Tikhomirov, A.2
  • 17
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • MR0144363
    • HOEFFDING, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 13-30. MR0144363
    • (1963) J. Amer. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 18
    • 52349112409 scopus 로고    scopus 로고
    • Spectra of sparse random matrices
    • 21. MR2455271
    • KÜHN, R. (2008). Spectra of sparse random matrices. J. Phys. A 41 295002, 21. MR2455271
    • (2008) J. Phys. A , vol.41 , pp. 295002
    • Kühn, R.1
  • 21
    • 36149035179 scopus 로고
    • Universality of level correlation function of sparse random matrices
    • MR1118532
    • MIRLIN, A. D. and FYODOROV, Y. V. (1991). Universality of level correlation function of sparse random matrices. J. Phys. A 24 2273-2286. MR1118532
    • (1991) J. Phys. A , vol.24 , pp. 2273-2286
    • Mirlin, A.D.1    Fyodorov, Y.V.2
  • 22
    • 51449120411 scopus 로고    scopus 로고
    • Spectral density of sparse sample covariance matrices
    • MR2341055
    • NAGAO, T. and TANAKA, T. (2007). Spectral density of sparse sample covariance matrices. J. Phys. A 40 4973-4987. MR2341055
    • (2007) J. Phys. A , vol.40 , pp. 4973-4987
    • Nagao, T.1    Tanaka, T.2
  • 23
    • 72549096261 scopus 로고    scopus 로고
    • Circular law, extreme singular values and potential theory
    • MR2575411
    • PAN, G. and ZHOU, W. (2010). Circular law, extreme singular values and potential theory. J. Multivariate Anal. 101 645-656. MR2575411
    • (2010) J. Multivariate Anal. , vol.101 , pp. 645-656
    • Pan, G.1    Zhou, W.2
  • 24
    • 0038568622 scopus 로고
    • Density of states of a sparse random matrix
    • MR0932406
    • RODGERS, G. J. and BRAY, A. J. (1988). Density of states of a sparse random matrix. Phys. Rev. B (3) 37 3557-3562. MR0932406
    • (1988) Phys. Rev. B (3) , vol.37 , pp. 3557-3562
    • Rodgers, G.J.1    Bray, A.J.2
  • 25
    • 78049429654 scopus 로고    scopus 로고
    • Universal sum and product rules for random matrices
    • 15. MR2742824
    • ROGERS, T. (2010). Universal sum and product rules for random matrices. J. Math. Phys. 51 093304, 15. MR2742824
    • (2010) J. Math. Phys. , vol.51 , pp. 093304
    • Rogers, T.1
  • 26
    • 60349130737 scopus 로고    scopus 로고
    • Cavity approach to the spectral density ofnonHermitian sparse matrices
    • ROGERS, T. and PÉREZ CASTILLO, I. (2009). Cavity approach to the spectral density ofnonHermitian sparse matrices. Phys. Rev. E (3) 79 012101.
    • (2009) Phys. Rev. e (3) , vol.79 , pp. 012101
    • Rogers, T.1    Pérez Castillo, I.2
  • 27
    • 51849106455 scopus 로고    scopus 로고
    • Cavity approach to the spectral density of sparse symmetric random matrices
    • 6. MR2496088
    • ROGERS, T., PÉREZ CASTILLO, I., KÜHN, R. and TAKEDA, K. (2008). Cavity approach to the spectral density of sparse symmetric random matrices. Phys. Rev. E(3)78031116, 6. MR2496088
    • (2008) Phys. Rev. E(3) , pp. 78031116
    • Rogers, T.1    Pérez Castillo, I.2    Kühn, R.3    Takeda, K.4
  • 28
    • 84879614059 scopus 로고
    • Asymptotic distribution ofeigenvalues and degeneration of sparse random matrices
    • MR0461616
    • SATO, S. and KOBAYASHI, K. (1976/77). Asymptotic distribution ofeigenvalues and degeneration of sparse random matrices. Bull. Math. Statist. 17 83-99. MR0461616
    • (1976) Bull. Math. Statist. , vol.17 , pp. 83-99
    • Sato, S.1    Kobayashi, K.2
  • 29
    • 0037076813 scopus 로고    scopus 로고
    • Sparse random matrices: The eigenvalue spectrum revisited
    • MR1916090
    • SEMERJIAN, G. and CUGLIANDOLO, L. F. (2002). Sparse random matrices: The eigenvalue spectrum revisited. J. Phys. A 35 4837-4851. MR1916090
    • (2002) J. Phys. A , vol.35 , pp. 4837-4851
    • Semerjian, G.1    Cugliandolo, L.F.2
  • 30
    • 70350418110 scopus 로고    scopus 로고
    • The Tracy-Widom law for some sparse random matrices
    • MR2545551
    • SODIN, S. (2009). The Tracy-Widom law for some sparse random matrices. J. Stat. Phys. 136 834-841. MR2545551
    • (2009) J. Stat. Phys. , vol.136 , pp. 834-841
    • Sodin, S.1
  • 32
    • 44249125025 scopus 로고    scopus 로고
    • Random matrices: The circular law
    • MR2409368
    • TAO, T. and VU, V. (2008). Random matrices: The circular law. Commun. Contemp. Math. 10 261-307. MR2409368
    • (2008) Commun. Contemp. Math. , vol.10 , pp. 261-307
    • Tao, T.1    Vu, V.2
  • 33
    • 68949196333 scopus 로고    scopus 로고
    • From the Littlewood-Offord problem to the circular law: Universality of the spectral distribution of random matrices
    • MR2507275
    • TAO, T. and VU, V. (2009). From the Littlewood-Offord problem to the circular law: Universality of the spectral distribution of random matrices. Bull. Amer. Math. Soc. (N. S.) 46 377-396. MR2507275
    • (2009) Bull. Amer. Math. Soc. (N. S.) , vol.46 , pp. 377-396
    • Tao, T.1    Vu, V.2
  • 34
    • 77957124985 scopus 로고    scopus 로고
    • Random matrices: Universality of ESDs and the circular law. with an appendix by Manjunath Krishnapur
    • MR2722794
    • TAO, T. and VU, V. (2010). Random matrices: Universality of ESDs and the circular law. With an appendix by Manjunath Krishnapur. Ann. Probab. 38 2023-2065. MR2722794
    • (2010) Ann. Probab. , vol.38 , pp. 2023-2065
    • Tao, T.1    Vu, V.2
  • 36
    • 0001560594 scopus 로고
    • On the distribution of the roots of certain symmetric matrices
    • MR0095527
    • WIGNER, E. P. (1958). On the distribution of the roots of certain symmetric matrices. Ann. of Math. (2) 67 325-327. MR0095527
    • (1958) Ann. of Math. (2) , vol.67 , pp. 325-327
    • Wigner, E.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.