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Volumn 109, Issue 3, 2012, Pages

Spectra of sparse non-Hermitian random matrices: An analytical solution

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; CONVERGENCE RATES; DEGREE OF SYMMETRY; EXACT RESULTS; GRAPH EDGES; NONMONOTONIC; RANDOM GRAPHS; RANDOM MATRICES; RANDOM MATRIX THEORY; RANDOM-MATRIX ENSEMBLES; SPARSE GRAPHS; TRANSPORT PROCESS;

EID: 84864272086     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.109.030602     Document Type: Article
Times cited : (54)

References (58)
  • 1
    • 0347094524 scopus 로고
    • NUPABL 0375-9474 10.1016/0375-9474(89)90558-7
    • V.V. Sokolov and V.G. Zelevinsky, Nucl. Phys. A504, 562 (1989); NUPABL 0375-9474 10.1016/0375-9474(89)90558-7
    • (1989) Nucl. Phys. , vol.504 , pp. 562
    • Sokolov, V.V.1    Zelevinsky, V.G.2
  • 5
    • 84864215152 scopus 로고    scopus 로고
    • arXiv:math/0611589.
    • I.M. Johnstone, arXiv:math/0611589.
    • Johnstone, I.M.1
  • 10
    • 0000840166 scopus 로고
    • ANMAAH 0003-486X 10.2307/1970079
    • E. Wigner, Ann. Math. 62, 548 (1955); ANMAAH 0003-486X 10.2307/1970079
    • (1955) Ann. Math. , vol.62 , pp. 548
    • Wigner, E.1
  • 11
    • 0001560594 scopus 로고
    • ANMAAH 0003-486X 10.2307/1970008
    • E. Wigner, Ann. Math. 67, 325 (1958). ANMAAH 0003-486X 10.2307/1970008
    • (1958) Ann. Math. , vol.67 , pp. 325
    • Wigner, E.1
  • 13
    • 0002111201 scopus 로고
    • [TPRBAU 0040-585X 10.1137/1130089
    • V.L. Girko [Theory Probab. Appl. TPRBAU 0040-585X 30, 677 (1986) (translated by Y. Ellis)]. 10.1137/1130089
    • (1986) Theory Probab. Appl. , vol.30 , pp. 677
    • Girko, V.L.1
  • 14
    • 0007805173 scopus 로고
    • LMSBBT 0024-6093 10.1112/blms/21.3.209
    • B. Mohar and W. Woess, Bull. Lond. Math. Soc. 21, 209 (1989). LMSBBT 0024-6093 10.1112/blms/21.3.209
    • (1989) Bull. Lond. Math. Soc. , vol.21 , pp. 209
    • Mohar, B.1    Woess, W.2
  • 15
    • 33847574798 scopus 로고
    • 0002-9947 10.1090/S0002-9947-1959-0109367-6
    • H. Kesten, Trans. Am. Math. Soc. 92, 336 (1959); 0002-9947 10.1090/S0002-9947-1959-0109367-6
    • (1959) Trans. Am. Math. Soc. , vol.92 , pp. 336
    • Kesten, H.1
  • 16
    • 0000294458 scopus 로고
    • LAAPAW 0024-3795 10.1016/0024-3795(81)90150-6
    • B.D. MacKay, Linear Algebra Appl. 40, 203 (1981). LAAPAW 0024-3795 10.1016/0024-3795(81)90150-6
    • (1981) Linear Algebra Appl. , vol.40 , pp. 203
    • MacKay, B.D.1
  • 17
    • 21144484097 scopus 로고
    • JMCHEG 0259-9791 10.1007/BF01164627
    • D.J. Klein and R. Randić, J. Math. Chem. 12, 81 (1993). JMCHEG 0259-9791 10.1007/BF01164627
    • (1993) J. Math. Chem. , vol.12 , pp. 81
    • Klein, D.J.1    Randić, R.2
  • 18
    • 0001884774 scopus 로고
    • PRLAAZ 1364-5021 10.1098/rspa.1982.0056
    • S.F. Edwards and D.R. Wilkinson, Proc. R. Soc. A 381, 17 (1982); PRLAAZ 1364-5021 10.1098/rspa.1982.0056
    • (1982) Proc. R. Soc. A , vol.381 , pp. 17
    • Edwards, S.F.1    Wilkinson, D.R.2
  • 19
    • 2142642287 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.92.108701
    • B. Kozma, M.B. Hastings, and G. Korniss, Phys. Rev. Lett. 92, 108701 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.108701
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 108701
    • Kozma, B.1    Hastings, M.B.2    Korniss, G.3
  • 22
    • 34250768646 scopus 로고    scopus 로고
    • JPAMB5 1751-8113 10.1088/1751-8113/40/27/F07
    • U. Smilansky, J. Phys. A 40, F621 (2007); JPAMB5 1751-8113 10.1088/1751-8113/40/27/F07
    • (2007) J. Phys. A , vol.40 , pp. 621
    • Smilansky, U.1
  • 23
    • 70449565304 scopus 로고    scopus 로고
    • JPAMB5 1751-8113 10.1088/1751-8113/42/41/415101
    • I. Oren, A. Godel, and U. Smilansky, J. Phys. A 42, 415101 (2009); JPAMB5 1751-8113 10.1088/1751-8113/42/41/415101
    • (2009) J. Phys. A , vol.42 , pp. 415101
    • Oren, I.1    Godel, A.2    Smilansky, U.3
  • 24
    • 77952921238 scopus 로고    scopus 로고
    • JPAMB5 1751-8113 10.1088/1751-8113/43/22/225205
    • I. Oren and U. Smilansky, J. Phys. A 43, 225205 (2010). JPAMB5 1751-8113 10.1088/1751-8113/43/22/225205
    • (2010) J. Phys. A , vol.43 , pp. 225205
    • Oren, I.1    Smilansky, U.2
  • 28
    • 60349130737 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.79.012101
    • T. Rogers and I.P. Castillo, Phys. Rev. E 79, 012101 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.79.012101
    • (2009) Phys. Rev. e , vol.79 , pp. 012101
    • Rogers, T.1    Castillo, I.P.2
  • 31
    • 80051478443 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.107.068702
    • I. Neri, N. Kern, and A. Parmeggiani, Phys. Rev. Lett. 107, 068702 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.068702
    • (2011) Phys. Rev. Lett. , vol.107 , pp. 068702
    • Neri, I.1    Kern, N.2    Parmeggiani, A.3
  • 33
    • 0001203841 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.67.941
    • N. Lehmann and H.-J. Sommers, Phys. Rev. Lett. 67, 941 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.67.941
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 941
    • Lehmann, N.1    Sommers, H.-J.2
  • 35
    • 3342992472 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.77.570
    • N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996); PRLTAO 0031-9007 10.1103/PhysRevLett.77.570
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 570
    • Hatano, N.1    Nelson, D.R.2
  • 36
    • 4243643447 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.76.1461
    • J. Miller and J. Wang, Phys. Rev. Lett. 76, 1461 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.1461
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 1461
    • Miller, J.1    Wang, J.2
  • 37
    • 0001365958 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.79.491
    • K.B. Efetov, Phys. Rev. Lett. 79, 491 (1997); PRLTAO 0031-9007 10.1103/PhysRevLett.79.491
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 491
    • Efetov, K.B.1
  • 38
    • 0642332297 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.56.9630
    • K.B. Efetov Phys. Rev. B 56, 9630 (1997). PRBMDO 0163-1829 10.1103/PhysRevB.56.9630
    • (1997) Phys. Rev. B , vol.56 , pp. 9630
    • Efetov, K.B.1
  • 39
    • 4244201369 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.61.1899
    • R. Grobe, F. Haake, and H.-J. Sommers, Phys. Rev. Lett. 61, 1899 (1988); PRLTAO 0031-9007 10.1103/PhysRevLett.61.1899
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 1899
    • Grobe, R.1    Haake, F.2    Sommers, H.-J.3
  • 40
    • 0001048690 scopus 로고
    • ZPCMDN 0722-3277 10.1007/BF01470925
    • F. Haake, F. Izrailev, and N. Lehmann, Z. Phys. B 88, 359 (1992); ZPCMDN 0722-3277 10.1007/BF01470925
    • (1992) Z. Phys. B , vol.88 , pp. 359
    • Haake, F.1    Izrailev, F.2    Lehmann, N.3
  • 41
    • 4244193270 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.62.2893
    • R.Grobe and F.Haake, Phys. Rev. Lett. 62, 2893 (1989). PRLTAO 0031-9007 10.1103/PhysRevLett.62.2893
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 2893
    • Grobe, R.1    Haake, F.2
  • 45
    • 0031551792 scopus 로고    scopus 로고
    • NUPBBO 0550-3213 10.1016/S0550-3213(97)00502-6
    • J. FeinBerg and A. Zee, Nucl. Phys. B504, 579 (1997). NUPBBO 0550-3213 10.1016/S0550-3213(97)00502-6
    • (1997) Nucl. Phys. , vol.504 , pp. 579
    • Feinberg, J.1    Zee, A.2
  • 46
    • 84864215150 scopus 로고    scopus 로고
    • See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.109.030602 for the derivation of the resolvent equations.
  • 47
    • 0001396998 scopus 로고
    • PRLAAZ 1364-5021 10.1098/rspa.1935.0122
    • H.A. Bethe, Proc. R. Soc. A 150, 552 (1935); PRLAAZ 1364-5021 10.1098/rspa.1935.0122
    • (1935) Proc. R. Soc. A , vol.150 , pp. 552
    • Bethe, H.A.1
  • 49
    • 84864184617 scopus 로고    scopus 로고
    • See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.109.030602 for solutions to the resolvent equations.
  • 50
    • 83255193032 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.84.055101
    • F.L. Metz, I. Neri, and D. Bollé, Phys. Rev. E 84, 055101(R) (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.055101
    • (2011) Phys. Rev. e , vol.84
    • Metz, F.L.1    Neri, I.2    Bollé, D.3
  • 51
    • 11544339752 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.80.5243
    • C.M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.5243
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 5243
    • Bender, C.M.1    Boettcher, S.2
  • 54
    • 84864203457 scopus 로고    scopus 로고
    • arXiv:1010.1726.
    • P.M. Wood, arXiv:1010.1726.
    • Wood, P.M.1
  • 56
    • 78651255820 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.82.031135
    • F.L. Metz, I. Neri, and D. Bollé, Phys. Rev. E 82, 031135 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.82.031135
    • (2010) Phys. Rev. e , vol.82 , pp. 031135
    • Metz, F.L.1    Neri, I.2    Bollé, D.3
  • 57
    • 70350418110 scopus 로고    scopus 로고
    • JSTPSB 0022-4715 10.1007/s10955-009-9813-2
    • S. Sodin, J. Stat. Phys. 136, 834 (2009); JSTPSB 0022-4715 10.1007/s10955-009-9813-2
    • (2009) J. Stat. Phys. , vol.136 , pp. 834
    • Sodin, S.1


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