메뉴 건너뛰기




Volumn 51, Issue 9, 2010, Pages

Universal sum and product rules for random matrices

Author keywords

[No Author keywords available]

Indexed keywords


EID: 78049429654     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3481569     Document Type: Article
Times cited : (28)

References (35)
  • 2
    • 21144462815 scopus 로고
    • CMPHAY, 0010-3616, 10.1007/BF02096955
    • Khorunzhy A. Pastur L. Commun. Math. Phys. 1993, 153:605. CMPHAY, 0010-3616, 10.1007/BF02096955, and.
    • (1993) Commun. Math. Phys. , vol.153 , pp. 605
    • Khorunzhy, A.1    Pastur, L.2
  • 4
    • 0002728029 scopus 로고
    • TMPHAH, 0040-5779, 10.1007/BF01035768.
    • Pastur L. Theor. Math. Phys. 1972, 10:67. TMPHAH, 0040-5779, 10.1007/BF01035768.
    • (1972) Theor. Math. Phys. , vol.10 , pp. 67
    • Pastur, L.1
  • 5
    • 0031534271 scopus 로고    scopus 로고
    • APBYAE, 0091-1798, 10.1214/aop/1024404298.
    • Bai Z. Ann. Probab. 1997, 25:494. APBYAE, 0091-1798, 10.1214/aop/1024404298.
    • (1997) Ann. Probab. , vol.25 , pp. 494
    • Bai, Z.1
  • 7
    • 0001393752 scopus 로고
    • TPRBAU, 0040-585X, 10.1137/1129095.
    • Girko V. Theor. Probab. Appl. 1985, 29:694. TPRBAU, 0040-585X, 10.1137/1129095.
    • (1985) Theor. Probab. Appl. , vol.29 , pp. 694
    • Girko, V.1
  • 10
    • 44249125025 scopus 로고    scopus 로고
    • ZZZZZZ, 0219-1997, 10.1142/S0219199708002788
    • Tao T. Vu V. Commun. Contemp. Math. 2008, 10:261. ZZZZZZ, 0219-1997, 10.1142/S0219199708002788, and.
    • (2008) Commun. Contemp. Math. , vol.10 , pp. 261
    • Tao, T.1    Vu, V.2
  • 11
    • 0001463454 scopus 로고    scopus 로고
    • PRLTAO, 0031-9007, 10.1103/PhysRevLett.76.4472.
    • Stephanov M. Phys. Rev. Lett. 1996, 76:4472. PRLTAO, 0031-9007, 10.1103/PhysRevLett.76.4472.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 4472
    • Stephanov, M.1
  • 12
    • 78049438410 scopus 로고    scopus 로고
    • Sometimes, for example, in Refs. 1718, this function, or its negative, is known as the resolvent.
    • Sometimes, for example, in Refs. 1718, this function, or its negative, is known as the resolvent.
  • 13
    • 78049451109 scopus 로고    scopus 로고
    • For instance, an electrostatic potential introduced in Ref. 29 and used frequently thereafter.
    • For instance, an electrostatic potential introduced in Ref. 29 and used frequently thereafter.
  • 14
    • 0031551792 scopus 로고    scopus 로고
    • NUPBBO, 0550-3213, 10.1016/S0550-3213(97)00502-6
    • Feinberg J. Zee A. Nucl. Phys. B 1997, 504:579. NUPBBO, 0550-3213, 10.1016/S0550-3213(97)00502-6, and.
    • (1997) Nucl. Phys. B , vol.504 , pp. 579
    • Feinberg, J.1    Zee, A.2
  • 15
    • 0031583545 scopus 로고    scopus 로고
    • NUPBBO, 0550-3213, 10.1016/S0550-3213(97)00419-7
    • Feinberg J. Zee A. Nucl. Phys. B 1997, 501:643. NUPBBO, 0550-3213, 10.1016/S0550-3213(97)00419-7, and.
    • (1997) Nucl. Phys. B , vol.501 , pp. 643
    • Feinberg, J.1    Zee, A.2
  • 17
    • 0001032742 scopus 로고    scopus 로고
    • PLEEE8, 1063-651X, 10.1103/PhysRevE.55.4100
    • Janik R. Nowak M. Papp G. Zahed I. Phys. Rev. E 1997, 55:4100. PLEEE8, 1063-651X, 10.1103/PhysRevE.55.4100, and.
    • (1997) Phys. Rev. E , vol.55 , pp. 4100
    • Janik, R.1    Nowak, M.2    Papp, G.3    Zahed, I.4
  • 18
    • 0031583540 scopus 로고    scopus 로고
    • NUPBBO, 0550-3213, 10.1016/S0550-3213(97)00418-5
    • Janik R. Nowak M. Papp G. Zahed I. Nucl. Phys. B 1997, 501:603. NUPBBO, 0550-3213, 10.1016/S0550-3213(97)00418-5, and.
    • (1997) Nucl. Phys. B , vol.501 , pp. 603
    • Janik, R.1    Nowak, M.2    Papp, G.3    Zahed, I.4
  • 19
    • 78049419588 scopus 로고    scopus 로고
    • e-print arXiv:math-ph/0402057.
    • Jarosz A. Nowak M. and e-print arXiv:math-ph/0402057.
    • Jarosz, A.1    Nowak, M.2
  • 20
    • 33746709969 scopus 로고    scopus 로고
    • JPHAC5, 0305-4470, 10.1088/0305-4470/39/32/S12
    • Jarosz A. Nowak M. J. Phys. A 2006, 39:10107. JPHAC5, 0305-4470, 10.1088/0305-4470/39/32/S12, and.
    • (2006) J. Phys. A , vol.39 , pp. 10107
    • Jarosz, A.1    Nowak, M.2
  • 21
    • 78049420797 scopus 로고    scopus 로고
    • e-print arXiv:math-ph/0408019.
    • Goerlich A. Jarosz A. and e-print arXiv:math-ph/0408019.
    • Goerlich, A.1    Jarosz, A.2
  • 23
    • 77951726950 scopus 로고    scopus 로고
    • PLEEE8, 1063-651X, 10.1103/PhysRevE.81.041132
    • Burda Z. Janik R. Waclaw B. Phys. Rev. E 2010, 81:041132. PLEEE8, 1063-651X, 10.1103/PhysRevE.81.041132, and.
    • (2010) Phys. Rev. E , vol.81 , pp. 041132
    • Burda, Z.1    Janik, R.2    Waclaw, B.3
  • 24
    • 78049425197 scopus 로고    scopus 로고
    • The Diablerets Winter School (unpublished notes available online at ).
    • Khoruzhenko B. 2003, The Diablerets Winter School (unpublished notes available online at ).
    • (2003)
    • Khoruzhenko, B.1
  • 25
    • 78149501031 scopus 로고    scopus 로고
    • Circular law for non-central random matrices
    • JTPREO, 0894-9840, (to be published).
    • Chafai D. Circular law for non-central random matrices. J. Theor. Probab. JTPREO, 0894-9840, (to be published).
    • J. Theor. Probab.
    • Chafai, D.1
  • 26
    • 78049418229 scopus 로고    scopus 로고
    • This result was also found independently by Haagerup nearly a decade ago; it appears in handwritten notes distributed at MSRI in , although the proof is substantially different.
    • 2001, This result was also found independently by Haagerup nearly a decade ago; it appears in handwritten notes distributed at MSRI in although the proof is substantially different.
    • (2001)
  • 27
    • 78049422842 scopus 로고    scopus 로고
    • In fact, the full jdpf of eigenvalues for matrices of this type was found recently in Ref. 35.
    • In fact, the full jdpf of eigenvalues for matrices of this type was found recently in Ref. 35.
  • 28
  • 30
    • 0000161184 scopus 로고    scopus 로고
    • JPHAC5, 0305-4470, 10.1088/0305-4470/29/7/003.
    • Khoruzhenko B. J. Phys. A 1996, 29:L165. JPHAC5, 0305-4470, 10.1088/0305-4470/29/7/003.
    • (1996) J. Phys. A , vol.29
    • Khoruzhenko, B.1
  • 31
    • 78049440406 scopus 로고    scopus 로고
    • Notice that although this choice fails technical assumption (D3), the result still appears to hold.
    • Notice that although this choice fails technical assumption (D3), the result still appears to hold.
  • 32
    • 0000324960 scopus 로고
    • SJMAEL, 0895-4798, 10.1137/0609045.
    • Edelman A. SIAM J. Matrix Anal. Appl. 1988, 9:543. SJMAEL, 0895-4798, 10.1137/0609045.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 543
    • Edelman, A.1
  • 33
    • 31444455248 scopus 로고    scopus 로고
    • AIHPA2, 0365-320X, 10.1016/j.anihpb.2005.04.001
    • Carmona P. Hu Y. Ann. Inst. Henri Poincare 2006, 42:215. AIHPA2, 0365-320X, 10.1016/j.anihpb.2005.04.001, and.
    • (2006) Ann. Inst. Henri Poincare , vol.42 , pp. 215
    • Carmona, P.1    Hu, Y.2
  • 34
    • 78049426599 scopus 로고    scopus 로고
    • Banded Toeplitz matrices are a good choice.
    • Banded Toeplitz matrices are a good choice.
  • 35
    • 63049135996 scopus 로고    scopus 로고
    • APBYAE, 0091-1798, 10.1214/08-AOP404.
    • Krishnapur M. Ann. Probab. 2009, 37:314. APBYAE, 0091-1798, 10.1214/08-AOP404.
    • (2009) Ann. Probab. , vol.37 , pp. 314
    • Krishnapur, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.