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Volumn 41, Issue 29, 2008, Pages

Spectra of sparse random matrices

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EID: 52349112409     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/29/295002     Document Type: Article
Times cited : (151)

References (54)
  • 1
    • 84927349471 scopus 로고
    • On the statistical distribution of the widths and spacings of nuclear resonance levels
    • Wigner E P 1951 On the statistical distribution of the widths and spacings of nuclear resonance levels Proc. Cam. Phil. Soc. 47 790-8
    • (1951) Proc. Cam. Phil. Soc. , vol.47 , pp. 790-798
    • Wigner, E.P.1
  • 2
    • 0015514970 scopus 로고
    • Will a large complex system be stable?
    • May R M 1972 Will a large complex system be stable? Nature 238 413-4
    • (1972) Nature , vol.238 , Issue.5364 , pp. 413-414
    • May, R.M.1
  • 3
    • 33646977864 scopus 로고
    • Maximum metallic resistance in thin wires
    • Thouless D J 1977 Maximum metallic resistance in thin wires Phys. Rev. Lett. 39 1167-9
    • (1977) Phys. Rev. Lett. , vol.39 , Issue.18 , pp. 1167-1169
    • Thouless, D.J.1
  • 4
    • 0346788422 scopus 로고
    • Characterization of chaotic quantum spectra and universality of level fluctuation laws
    • Bohigas O, Giannoni M J and Schmit C 1984 Characterization of chaotic quantum spectra and universality of level fluctuation laws Phys. Rev. Lett. 52 1-4 (DOI:D10.1103/PhysRevLett.52.1)
    • (1984) Phys. Rev. Lett. , vol.52 , Issue.1 , pp. 1-4
    • Bohigas, O.1    Giannoni, M.J.2    Schmit, C.3
  • 5
    • 4243561258 scopus 로고
    • The spectrum of the QCD dirac operator and chiral random matrix theory: The threefold way
    • Verbaarschot J 1994 The spectrum of the QCD dirac operator and chiral random matrix theory: the threefold way Phys. Rev. Lett. 72 2531-3
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.16 , pp. 2531-2533
    • Verbaarschot, J.1
  • 7
    • 0000656722 scopus 로고    scopus 로고
    • Universal and non-universal properties of cross-correlations in financial time series
    • Plerou V, Gopikrishnan P, Rosenow B, Amaral L A N and Stanley H E 1999 Universal and non-universal properties of cross-correlations in financial time series Phys. Rev. Lett. 83 1471-4
    • (1999) Phys. Rev. Lett. , vol.83 , Issue.7 , pp. 1471-1474
    • Plerou, V.1    Gopikrishnan, P.2    Rosenow, B.3    Amaral, L.A.N.4    Stanley, H.E.5
  • 8
    • 1642425555 scopus 로고    scopus 로고
    • Analytic computation of the instantaneous normal modes spectrum in low density liquids
    • Cavagna A, Giardina I and Parisi G 1999 Analytic computation of the instantaneous normal modes spectrum in low density liquids Phys. Rev. Lett. 83 108-11
    • (1999) Phys. Rev. Lett. , vol.83 , Issue.1 , pp. 108-111
    • Cavagna, A.1    Giardina, I.2    Parisi, G.3
  • 10
    • 0038610765 scopus 로고    scopus 로고
    • Random matrix approach to glassy physics: Low temperatures and beyond
    • Kühn R and Horstmann U 1997 Random matrix approach to glassy physics: low temperatures and beyond Phys. Rev. Lett. 78 4067-70
    • (1997) Phys. Rev. Lett. , vol.78 , Issue.21 , pp. 4067-4070
    • Kühn, R.1    Horstmann, U.2
  • 11
    • 0037657944 scopus 로고    scopus 로고
    • Universality in glassy low-temperature physics
    • Kühn R 2003 Universality in glassy low-temperature physics Europhys. Lett. 62 313-9
    • (2003) Europhys. Lett. , vol.62 , Issue.3 , pp. 313-319
    • Kühn, R.1
  • 12
    • 0034348205 scopus 로고    scopus 로고
    • Random matrix theory and L-functions at s = 1/2
    • Keating J P and Snaith N C 2000 Random matrix theory and L-functions at s = 1/2 Commun. Math. Phys. 214 91-110
    • (2000) Commun. Math. Phys. , vol.214 , Issue.1 , pp. 91-110
    • Keating, J.P.1    Snaith, N.C.2
  • 13
    • 0039165794 scopus 로고    scopus 로고
    • Random matrix theories in quantum physics: Common concepts
    • Guhr T, Müller-Groeling A and Weidenmüller H A 1998 Random matrix theories in quantum physics: common concepts Phys. Rep. 299 190-425
    • (1998) Phys. Rep. , vol.299 , Issue.4-6 , pp. 189-425
    • Guhr, T.1    Müller-Groeling, A.2    Weidenmüller, H.A.3
  • 14
    • 0038568622 scopus 로고
    • Density of states of a sparse random matrix
    • Rodgers G J and Bray A J 1988 Density of states of a sparse random matrix Phys. Rev. B 37 3557-62
    • (1988) Phys. Rev. , vol.37 , Issue.7 , pp. 3557-3562
    • Rodgers, G.J.1    Bray, A.J.2
  • 15
    • 0001714858 scopus 로고
    • Diffusion in a sparsely connected space: A model for glassy relaxation
    • Bray A J and Rodgers G J 1988 Diffusion in a sparsely connected space: a model for glassy relaxation Phys. Rev. B 38 11461-70
    • (1988) Phys. Rev. , vol.38 , Issue.16 , pp. 11461-11470
    • Bray, A.J.1    Rodgers, G.J.2
  • 16
    • 0036013593 scopus 로고    scopus 로고
    • Statistical mechanics of complex networks
    • Albert R and Barabsi A-L 2002 Statistical mechanics of complex networks Rev. Mod. Phys. 74 47-97
    • (2002) Rev. Mod. Phys. , vol.74 , Issue.1 , pp. 47-97
    • Albert, R.1    Barabsi, A.-L.2
  • 19
    • 33645671984 scopus 로고    scopus 로고
    • Lifshitz tails for spectra of Erdös-Renyi random graphs
    • Khorunzhiy O, Kirsch W and Müller P 2006 Lifshitz tails for spectra of Erdös-Renyi random graphs Ann. Appl. Prob. 16 295-309 (Preprint math-ph/0502054)
    • (2006) Ann. Appl. Prob. , vol.16 , Issue.1 , pp. 295-309
    • Khorunzhiy, O.1    Kirsch, W.2    Müller, P.3
  • 20
    • 0014667053 scopus 로고
    • Nonanalytic behavior above the critical point in a random Ising ferromagnet
    • Griffiths R B 1969 Nonanalytic behavior above the critical point in a random Ising ferromagnet Phys. Rev. Lett. 23 17-9
    • (1969) Phys. Rev. Lett. , vol.23 , Issue.1 , pp. 17-19
    • Griffiths, R.B.1
  • 21
    • 0003072651 scopus 로고
    • Spectral density singularities, level statistics and localization in a sparse random matrix ensemble
    • Evangelou S N and Economou E N 1992 Spectral density singularities, level statistics and localization in a sparse random matrix ensemble Phys. Rev. Lett. 68 361-4
    • (1992) Phys. Rev. Lett. , vol.68 , Issue.3 , pp. 361-364
    • Evangelou, S.N.1    Economou, E.N.2
  • 23
    • 0039885992 scopus 로고
    • On the density of states of sparse random matrices
    • Fyodorov Y V and Mirlin A D 1991 On the density of states of sparse random matrices J. Phys. A: Math. Gen. 24 2219-23
    • (1991) J. Phys. A: Math. Gen. , vol.24 , Issue.9 , pp. 2219-2223
    • Fyodorov, Y.V.1    Mirlin, A.D.2
  • 24
    • 2142640772 scopus 로고    scopus 로고
    • Eigebvalue distribution of large weighted random graphs
    • Khorunzhy O, Shcherbiba M and Vengerovsky V 2004 Eigebvalue distribution of large weighted random graphs J. Math. Phys. 45 1648-72
    • (2004) J. Math. Phys. , vol.45 , Issue.4 , pp. 1648-1672
    • Khorunzhy, O.1    Shcherbiba, M.2    Vengerovsky, V.3
  • 25
    • 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. Math. 67 325-7
    • (1958) Ann. Math. , vol.67 , Issue.2 , pp. 325-327
    • Wigner, E.P.1
  • 26
    • 0033580741 scopus 로고    scopus 로고
    • A single defect approximation for localized states on random lattices
    • Biroli G and Monasson R 1999 A single defect approximation for localized states on random lattices J. Phys. A: Math. Gen. 32 L255-61
    • (1999) J. Phys. A: Math. Gen. , vol.32 , Issue.24
    • Biroli, G.1    Monasson, R.2
  • 27
    • 0037076813 scopus 로고    scopus 로고
    • Sparse random matrices: The eigenvalue spectrum revisited
    • Semerjian G and Cugliandolo L F 2002 Sparse random matrices: the eigenvalue spectrum revisited J. Phys. A: Math. Gen. 35 4837-51
    • (2002) J. Phys. A: Math. Gen. , vol.35 , Issue.23 , pp. 4837-4851
    • Semerjian, G.1    Cugliandolo, L.F.2
  • 29
    • 4043141148 scopus 로고    scopus 로고
    • Spectra and eigenvectors of scale-free networks
    • Goh K-I, Kahng B and Kim D 2001 Spectra and eigenvectors of scale-free networks Phys. Rev. E 64 051903
    • (2001) Phys. Rev. , vol.64 , Issue.5 , pp. 051903
    • Goh, K.-I.1    Kahng, B.2    Kim, D.3
  • 30
    • 0040426391 scopus 로고    scopus 로고
    • Optimization problems and replica symmetry breaking in finite connectivity spin-glasses
    • Monasson R 1998 Optimization problems and replica symmetry breaking in finite connectivity spin-glasses J. Phys. A: Math. Gen. 31 513-29
    • (1998) J. Phys. A: Math. Gen. , vol.31 , Issue.2 , pp. 513-529
    • Monasson, R.1
  • 31
    • 0038401954 scopus 로고    scopus 로고
    • The Bethe lattice spin glass revisited
    • Mézard M and Parisi G 2001 The Bethe lattice spin glass revisited Eur. Phys. J. B 20 217-33 (DOI:10.1007/PL00011099)
    • (2001) Eur. Phys. J. , vol.20 , Issue.2 , pp. 217-233
    • Mézard, M.1    Parisi, G.2
  • 33
    • 34547472589 scopus 로고    scopus 로고
    • Finitely coordinated models for low-temperature phases of amorphous systems
    • Kühn R, van Mourik J, Weigt M and Zippelius A 2007 Finitely coordinated models for low-temperature phases of amorphous systems J. Phys. A: Math. Theor. 40 9227-52
    • (2007) J. Phys. A: Math. Theor. , vol.40 , Issue.31 , pp. 9227-9252
    • Kühn, R.1    Van Mourik, J.2    Weigt, M.3    Zippelius, A.4
  • 34
    • 0001179672 scopus 로고
    • The eigenvalue spectrum of a large symmetric random matrix
    • Edwards S F and Jones R C 1976 The eigenvalue spectrum of a large symmetric random matrix J. Phys. A: Math. Gen. 9 1595-603
    • (1976) J. Phys. A: Math. Gen. , vol.9 , Issue.10 , pp. 1595-1603
    • Edwards, S.F.1    Jones, R.C.2
  • 39
    • 65549088216 scopus 로고
    • Phase diagrams for dilute spin glasses
    • Viana L and Bray A J 1985 Phase diagrams for dilute spin glasses J. Phys. C: Solid State Phys. 18 3037-51
    • (1985) J. Phys. C: Solid State Phys. , vol.18 , Issue.15 , pp. 3037-3051
    • Viana, L.1    Bray, A.J.2
  • 40
    • 0001775471 scopus 로고
    • Mean-field theory of spin-glasses with finite ccoordination number
    • Kanter I and Sompolinsky H 1987 Mean-field theory of spin-glasses with finite ccoordination number Phys. Rev. Lett. 58 164-7
    • (1987) Phys. Rev. Lett. , vol.58 , Issue.2 , pp. 164-167
    • Kanter, I.1    Sompolinsky, H.2
  • 41
    • 0030246717 scopus 로고    scopus 로고
    • Randomly crosslinked macromolecular systems: Vulcanisation transition to and properties of the amorphous solid state
    • Goldbart P M, Castillo H M and Zippelius A 1996 Randomly crosslinked macromolecular systems: vulcanisation transition to and properties of the amorphous solid state Adv. Phys. 45 393-468
    • (1996) Adv. Phys. , vol.45 , Issue.5 , pp. 393-468
    • Goldbart, P.M.1    Castillo, H.M.2    Zippelius, A.3
  • 42
    • 21144466780 scopus 로고
    • A numerical study of sparse random matrices
    • Evangelou S N 1992 A numerical study of sparse random matrices J. Stat. Phys. 69 361-83
    • (1992) J. Stat. Phys. , vol.69 , Issue.1-2 , pp. 361-383
    • Evangelou, S.N.1
  • 43
    • 5844284048 scopus 로고
    • The theory of impurity conduction
    • Mott N F and Twose W D 1961 The theory of impurity conduction Adv. Phys. 10 107-63
    • (1961) Adv. Phys. , vol.10 , Issue.38 , pp. 107-163
    • Mott, N.F.1    Twose, W.D.2
  • 45
    • 0000294458 scopus 로고
    • The expected eigenvalue distribution of a large regular graph
    • McKay B D 1981 The expected eigenvalue distribution of a large regular graph Linear Algebr. Appl. 40 203-16
    • (1981) Linear Algebr. Appl. , vol.40 , Issue.1 , pp. 203-216
    • McKay, B.D.1
  • 48
    • 0037864401 scopus 로고    scopus 로고
    • Random symmetric matrices with a constraint: The spectral density of random impedance networks
    • Stäring J, Mehlig B, Fyodorov Y V and Luck J M 2003 Random symmetric matrices with a constraint: the spectral density of random impedance networks Phys. Rev. E 67 047101
    • (2003) Phys. Rev. , vol.67 , Issue.4 , pp. 047101
    • Stäring, J.1    Mehlig, B.2    Fyodorov, Y.V.3    Luck, J.M.4
  • 49
    • 36149035179 scopus 로고
    • Universality of level correlation function of sparse random matrices
    • Mirlin A D and Fyodorov Y V 1991 Universality of level correlation function of sparse random matrices J. Phys. A: Math. Gen. 24 2273-86
    • (1991) J. Phys. A: Math. Gen. , vol.24 , Issue.10 , pp. 2273-2286
    • Mirlin, A.D.1    Fyodorov, Y.V.2
  • 50
    • 0033595656 scopus 로고    scopus 로고
    • Spectral properties of random reactance networks and random matrix pencils
    • Fyodorov Y V 1999 Spectral properties of random reactance networks and random matrix pencils J. Phys. A: Math. Gen. 32 7429-46
    • (1999) J. Phys. A: Math. Gen. , vol.32 , Issue.42 , pp. 7429-7446
    • Fyodorov, Y.V.1
  • 51
    • 0001048690 scopus 로고
    • Statistics of complex levels of random matrices for decaying systems
    • Haake F, Izrailev F, Lehmann N, Saher D and Sommers H-J 1992 Statistics of complex levels of random matrices for decaying systems Z. Phys. B 88 359-70
    • (1992) Z. Phys. , vol.88 , Issue.3 , pp. 359-370
    • Haake, F.1    Izrailev, F.2    Lehmann, N.3    Saher, D.4    Sommers, H.-J.5


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