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Volumn 15, Issue , 2010, Pages 526-603

Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation

Author keywords

Dyson sine kernel; Wigner random matrix

Indexed keywords


EID: 77953158852     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v15-768     Document Type: Article
Times cited : (59)

References (30)
  • 2
    • 0001119849 scopus 로고
    • Diffusions hypercontractives
    • 1983/84, 1123 Lecture Notes in Mathematics, Springer, Berlin
    • Bakry, D., Émery, M.: Diffusions hypercontractives. in: Séminaire de probabilités, XIX, 1983/84, 1123 Lecture Notes in Mathematics, Springer, Berlin, 1985, 177-206.
    • (1985) Séminaire De probabilités, XIX , pp. 177-206
    • Bakry, D.1    Émery, M.2
  • 3
    • 77953174549 scopus 로고    scopus 로고
    • Universality of local eigenvalue statistics for some sample covariance matrices
    • Ben Arous, G., Péché, S.: Universality of local eigenvalue statistics for some sample covariance matrices. Comm. PureAppl. Math.vol LVIII. (2005), 1-42.
    • (2005) Comm. Pureappl. Math , vol.LVIII , pp. 1-42
    • Ben Arous, G.1    Péché, S.2
  • 4
    • 0002829137 scopus 로고    scopus 로고
    • Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
    • Bobkov, S. G., Götze, F.: Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal. 163 (1999), no. 1, 1-28.
    • (1999) J. Funct. Anal , vol.163 , Issue.1 , pp. 1-28
    • Bobkov, S.G.1    Götze, F.2
  • 6
    • 84868036270 scopus 로고    scopus 로고
    • Asymptotic distribution of smoothed eigenvalue density. II. Wigner random matrices
    • Boutet de Monvel, A., Khorunzhy, A.: Asymptotic distribution of smoothed eigenvalue density. II. Wigner random matrices. Random Oper, and Stoch. Equ., 7 No. 2, (1999), 149-168.
    • (1999) Random Oper, and Stoch. Equ. , vol.7 , Issue.2 , pp. 149-168
    • Boutet De Monvel, A.1    Khorunzhy, A.2
  • 7
    • 0030592669 scopus 로고    scopus 로고
    • Correlations of nearby levels induced by a random potential
    • and Spectral form factor in a random matrix theory. Phys. Rev. E 55 (1997), 4067-4083
    • Brézin, E., Hikami, S.: Correlations of nearby levels induced by a random potential. Nucl. Phys. B 479 (1996), 697-706, and Spectral form factor in a random matrix theory. Phys. Rev. E 55 (1997), 4067-4083.
    • (1996) Nucl. Phys. B , vol.479 , pp. 697-706
    • Brézin, E.1    Hikami, S.2
  • 8
    • 0000787440 scopus 로고
    • The functional calculus
    • Davies, E.B.: The functional calculus. J. London Math. Soc. (2) 52 (1) (1995), 166-176.
    • (1995) J. London Math. Soc. , vol.52 , Issue.1-2 , pp. 166-176
    • Davies, E.B.1
  • 9
    • 0003608444 scopus 로고    scopus 로고
    • Orthogonal polynomials and random matrices: A Riemann-Hilbert approach
    • American Mathematical Society, Providence, RI
    • Deift, P: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach. Courant Lecture Notes in Mathematics 3, American Mathematical Society, Providence, RI, 1999
    • (1999) Courant Lecture Notes in Mathematics 3
    • Deift, P.1
  • 10
    • 35549006412 scopus 로고
    • Statistical theory of energy levels of complex systems, I, II, and III
    • Dyson, F.J.: Statistical theory of energy levels of complex systems, I, II, and III. J. Math. Phys. 3, 140-156, 157-165, 166-175 (1962).
    • (1962) J. Math. Phys. , vol.3
    • Dyson, F.J.1
  • 11
    • 0041637573 scopus 로고
    • A Brownian-motion model for the eigenvalues of a random matrix
    • Dyson, F.J.: A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys. 3, 1191-1198 (1962).
    • (1962) J. Math. Phys , vol.3 , pp. 1191-1198
    • Dyson, F.J.1
  • 12
    • 0030568043 scopus 로고    scopus 로고
    • Navier-Stokes equation for stochastic particle systems on the lattice
    • Esposito, R., Marra, R., Yau, H.-T.: Navier-Stokes equation for stochastic particle systems on the lattice. Commun. Math. Phys. (1996) 182, no.2, 395-456.
    • (1996) Commun. Math. Phys , vol.182 , Issue.2 , pp. 395-456
    • Esposito, R.1    Marra, R.2    Yau, H.-T.3
  • 13
    • 77949568197 scopus 로고    scopus 로고
    • Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
    • Erdos, L., Schlein, B., Yau, H.-T.: Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Ann. Probab. 37, No. 3, 815-852 (2008)
    • (2008) Ann. Probab , vol.37 , Issue.3 , pp. 815-852
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 14
    • 61549110549 scopus 로고    scopus 로고
    • Local semicircle law and complete delocalization for Wigner random matrices
    • Erdos, L., Schlein, B., Yau, H.-T.: Local semicircle law and complete delocalization for Wigner random matrices. Commun. Math. Phys. 287, 641-655 (2009)
    • (2009) Commun. Math. Phys , vol.287 , pp. 641-655
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 15
    • 77953168459 scopus 로고    scopus 로고
    • Wegner estimate and level repulsion for Wigner random matrices
    • Erdos, L., Schlein, B., Yau, H.-T.: Wegner estimate and level repulsion for Wigner random matrices. Int. Math. Res. Not., Vol. 2010, No. 3, 436-479 (2010).
    • (2010) Int. Math. Res. Not. , vol.2010 , Issue.3 , pp. 436-479
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 18
    • 0001226135 scopus 로고    scopus 로고
    • Concentration of the spectral measure for large matrices
    • Paper 14
    • Guionnet, A., Zeitouni, O.: Concentration of the spectral measure for large matrices. Electronic Comm. in Probability 5 (2000) Paper 14.
    • (2000) Electronic Comm. In Probability , vol.5
    • Guionnet, A.1    Zeitouni, O.2
  • 20
    • 0003078083 scopus 로고
    • Nonlinear diffusion limit for a system with nearest neighbor interactions
    • Guo, M.Z., Papanicolaou, G.C., Varadhan, S.R.S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun. Math. Phys. 118 (1988) no.1, 31-59.
    • (1988) Commun. Math. Phys , vol.118 , Issue.1 , pp. 31-59
    • Guo, M.Z.1    Papanicolaou, G.C.2    Varadhan, S.R.S.3
  • 21
    • 0035530553 scopus 로고    scopus 로고
    • Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices
    • Johansson, K.: Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices. Comm. Math. Phys. 215 (2001), no.3. 683-705.
    • (2001) Comm. Math. Phys , vol.215 , Issue.3 , pp. 683-705
    • Johansson, K.1
  • 22
    • 0038609707 scopus 로고    scopus 로고
    • The concentration of measure phenomenon
    • American Mathematical Society, Providence, RI
    • Ledoux, M.: The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89 American Mathematical Society, Providence, RI, 2001.
    • (2001) Mathematical Surveys and Monographs , pp. 89
    • Ledoux, M.1
  • 23
    • 50349090048 scopus 로고    scopus 로고
    • Universality limits in the bulk for varying measures
    • Levin, E., Lubinsky S. D.: Universality limits in the bulk for varying measures. Adv. Math. 219 (2008), 743-779.
    • (2008) Adv. Math. , vol.219 , pp. 743-779
    • Levin, E.1    Lubinsky, S.D.2
  • 24
    • 84952981197 scopus 로고    scopus 로고
    • Orthogonal polynomials for exponential weights
    • Levin, E., Lubinsky, S. D.: Orthogonal polynomials for exponential weights. Springer 2001.
    • (2001) Springer
    • Levin, E.1    Lubinsky, S.D.2
  • 26
    • 36649018694 scopus 로고    scopus 로고
    • Bulk universality and related properties of Hermitian matrix models
    • Pastur, L., Shcherbina M.: Bulk universality and related properties of Hermitian matrix models. J. Stat. Phys. 130 (2008), no.2., 205-250.
    • (2008) J. Stat. Phys. , vol.130 , Issue.2 , pp. 205-250
    • Pastur, L.1    Shcherbina, M.2
  • 27
    • 0032334703 scopus 로고    scopus 로고
    • Lattice gases, large deviations and the incompressible Navier-Stokes equations
    • Quastel, J., Yau, H.T.: Lattice gases, large deviations and the incompressible Navier-Stokes equations. Ann. Of Math. (2) 148 (1998), no.1, 51-108.
    • (1998) Ann. Of Math. , vol.148 , Issue.1-2 , pp. 51-108
    • Quastel, J.1    Yau, H.T.2
  • 28
    • 0033473406 scopus 로고    scopus 로고
    • Universality at the edge of the spectrum in Wigner random matrices
    • Soshnikov, A.: Universality at the edge of the spectrum in Wigner random matrices. Comm. Math. Phys. 207 (1999), no.3. 697-733.
    • (1999) Comm. Math. Phys. , vol.207 , Issue.3 , pp. 697-733
    • Soshnikov, A.1
  • 30
    • 0000840166 scopus 로고
    • Characteristic vectors of bordered matrices with infinite dimensions
    • Wigner, E.: Characteristic vectors of bordered matrices with infinite dimensions. Ann. Of Math. 62 (1955), 548-564.
    • (1955) Ann. Of Math. , vol.62 , pp. 548-564
    • Wigner, E.1


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