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Volumn 229, Issue 3, 2012, Pages 1435-1515

Rigidity of eigenvalues of generalized Wigner matrices

Author keywords

Dyson Brownian motion; Local semicircle law; Random matrix; Tracy Widom distribution

Indexed keywords


EID: 84055178439     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2011.12.010     Document Type: Article
Times cited : (357)

References (46)
  • 1
    • 0036459716 scopus 로고    scopus 로고
    • On the concentration of eigenvalues of random symmetric matrices
    • Alon N., Krivelich M., Vu V. On the concentration of eigenvalues of random symmetric matrices. Israel J. Math. 2002, 131:259-267.
    • (2002) Israel J. Math. , vol.131 , pp. 259-267
    • Alon, N.1    Krivelich, M.2    Vu, V.3
  • 2
    • 77956169516 scopus 로고    scopus 로고
    • An Introduction to Random Matrices
    • Cambridge University Press
    • Anderson G., Guionnet A., Zeitouni O. An Introduction to Random Matrices. Stud. Adv. Math. 2009, vol. 118. Cambridge University Press.
    • (2009) Stud. Adv. Math. , vol.118
    • Anderson, G.1    Guionnet, A.2    Zeitouni, O.3
  • 5
    • 0242323254 scopus 로고    scopus 로고
    • Convergence rates of the spectral distributions of large Wigner matrices
    • Bai Z.D., Miao B., Tsay J. Convergence rates of the spectral distributions of large Wigner matrices. Int. Math. J. 2002, 1(1):65-90.
    • (2002) Int. Math. J. , vol.1 , Issue.1 , pp. 65-90
    • Bai, Z.D.1    Miao, B.2    Tsay, J.3
  • 6
    • 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. Pure Appl. Math. 2005, LVIII:1-42.
    • (2005) Comm. Pure Appl. Math. , vol.48 , pp. 1-42
    • Ben Arous, G.1    Péché, S.2
  • 7
    • 79051471398 scopus 로고    scopus 로고
    • On the top eigenvalue of heavy-tailed random matrices
    • Biroli G., Bouchaud J.-P., Potters M. On the top eigenvalue of heavy-tailed random matrices. Europhys. Lett. 2007, 78:10001.
    • (2007) Europhys. Lett. , vol.78 , pp. 10001
    • Biroli, G.1    Bouchaud, J.-P.2    Potters, M.3
  • 8
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
    • Bleher P., Its A. Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. 1999, 150:185-266.
    • (1999) Ann. of Math. , vol.150 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 9
    • 0030592669 scopus 로고    scopus 로고
    • Correlations of nearby levels induced by a random potential
    • Brézin E., Hikami S. Correlations of nearby levels induced by a random potential. Nuclear Phys. B 1996, 479:697-706.
    • (1996) Nuclear Phys. B , vol.479 , pp. 697-706
    • Brézin, E.1    Hikami, S.2
  • 10
    • 0001184776 scopus 로고    scopus 로고
    • Spectral form factor in a random matrix theory
    • Brézin E., Hikami S. Spectral form factor in a random matrix theory. Phys. Rev. E 1997, 55:4067-4083.
    • (1997) Phys. Rev. E , vol.55 , pp. 4067-4083
    • Brézin, E.1    Hikami, S.2
  • 11
    • 0003346458 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 Lect. Notes Math. 1999, vol. 3. American Mathematical Society, Providence, RI.
    • (1999) Courant Lect. Notes Math. , vol.3
    • Deift, P.1
  • 12
    • 79953750532 scopus 로고    scopus 로고
    • Random Matrix Theory: Invariant Ensembles and Universality
    • American Mathematical Society, Providence, RI
    • Deift P., Gioev D. Random Matrix Theory: Invariant Ensembles and Universality. Courant Lect. Notes Math. 2009, vol. 18. American Mathematical Society, Providence, RI.
    • (2009) Courant Lect. Notes Math. , vol.18
    • Deift, P.1    Gioev, D.2
  • 13
    • 0033440723 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
    • Deift P., Kriecherbauer T., McLaughlin K.T.-R., Venakides S., Zhou X. Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 1999, 52:1335-1425.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.5
  • 16
    • 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. 1962, 3:1191-1198.
    • (1962) J. Math. Phys. , vol.3 , pp. 1191-1198
    • Dyson, F.J.1
  • 18
    • 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. 2009, 37(3):815-852.
    • (2009) Ann. Probab. , vol.37 , Issue.3 , pp. 815-852
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 19
    • 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. Comm. Math. Phys. 2009, 287:641-655.
    • (2009) Comm. Math. Phys. , vol.287 , pp. 641-655
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 20
    • 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. 2010, 2010(3):436-479.
    • (2010) Int. Math. Res. Not. , vol.2010 , Issue.3 , pp. 436-479
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 21
    • 79959217986 scopus 로고    scopus 로고
    • Universality of random matrices and local relaxation flow
    • Erdos L., Schlein B., Yau H.-T. Universality of random matrices and local relaxation flow. Invent. Math. 2011, 185(1):75-119.
    • (2011) Invent. Math. , vol.185 , Issue.1 , pp. 75-119
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3
  • 22
    • 84855592446 scopus 로고    scopus 로고
    • The local relaxation flow approach to universality of the local statistics for random matrices, Ann. Inst. H. Poincaré Probab. Statist., in press, .
    • L. Erdos, B. Schlein, H.-T. Yau, J. Yin, The local relaxation flow approach to universality of the local statistics for random matrices, Ann. Inst. H. Poincaré Probab. Statist., in press, arxiv:0911.3687.
    • Erdos, L.1    Schlein, B.2    Yau, H.-T.3    Yin, J.4
  • 23
    • 84855612683 scopus 로고    scopus 로고
    • Universality for generalized Wigner matrices with Bernoulli distribution
    • Erdos L., Yau H.-T., Yin J. Universality for generalized Wigner matrices with Bernoulli distribution. J. Comb. 2011, 1(2):15-85.
    • (2011) J. Comb. , vol.1 , Issue.2 , pp. 15-85
    • Erdos, L.1    Yau, H.-T.2    Yin, J.3
  • 24
    • 84855592440 scopus 로고    scopus 로고
    • Bulk universality for generalized Wigner matrices, Probab. Theory Related Fields, in press, .
    • L. Erdos, H.-T. Yau, J. Yin, Bulk universality for generalized Wigner matrices, Probab. Theory Related Fields, in press, arxiv:1001.3453.
    • Erdos, L.1    Yau, H.-T.2    Yin, J.3
  • 25
    • 0036206682 scopus 로고    scopus 로고
    • Large deviation upper bounds and central limit theorems for band matrices
    • Guionnet A. Large deviation upper bounds and central limit theorems for band matrices. Ann. Inst. H. Poincaré Probab. Statist. 2002, 38:341-384.
    • (2002) Ann. Inst. H. Poincaré Probab. Statist. , vol.38 , pp. 341-384
    • Guionnet, A.1
  • 26
    • 14544296548 scopus 로고    scopus 로고
    • Gaussian fluctuations of eigenvalues in the GUE
    • Gustavsson J. Gaussian fluctuations of eigenvalues in the GUE. Ann. Inst. H. Poincaré Probab. Statist. 2005, 41(2):151-178.
    • (2005) Ann. Inst. H. Poincaré Probab. Statist. , vol.41 , Issue.2 , pp. 151-178
    • Gustavsson, J.1
  • 27
    • 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. 2001, 215(3):683-705.
    • (2001) Comm. Math. Phys. , vol.215 , Issue.3 , pp. 683-705
    • Johansson, K.1
  • 30
    • 77949568579 scopus 로고    scopus 로고
    • Gaussian fluctuations of eigenvalues in Wigner random matrices
    • O'Rourke S. Gaussian fluctuations of eigenvalues in Wigner random matrices. J. Stat. Phys. 2009, 138(6):1045-1066.
    • (2009) J. Stat. Phys. , vol.138 , Issue.6 , pp. 1045-1066
    • O'Rourke, S.1
  • 31
    • 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. 2008, 130(2):205-250.
    • (2008) J. Stat. Phys. , vol.130 , Issue.2 , pp. 205-250
    • Pastur, L.1    Shcherbina, M.2
  • 32
    • 36448958660 scopus 로고    scopus 로고
    • Wigner random matrices with non-symmetrically distributed entries
    • Péché S., Soshnikov A. Wigner random matrices with non-symmetrically distributed entries. J. Stat. Phys. 2007, 129(5-6):857-884.
    • (2007) J. Stat. Phys. , vol.129 , Issue.5-6 , pp. 857-884
    • Péché, S.1    Soshnikov, A.2
  • 33
    • 45149083670 scopus 로고    scopus 로고
    • On the lower bound of the spectral norm of symmetric random matrices with independent entries
    • Péché S., Soshnikov A. On the lower bound of the spectral norm of symmetric random matrices with independent entries. Electron. Commun. Probab. 2008, 13:280-290.
    • (2008) Electron. Commun. Probab. , vol.13 , pp. 280-290
    • Péché, S.1    Soshnikov, A.2
  • 34
    • 28144459476 scopus 로고    scopus 로고
    • Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries
    • Ruzmaikina A. Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries. Comm. Math. Phys. 2006, 261(2):277-296.
    • (2006) Comm. Math. Phys. , vol.261 , Issue.2 , pp. 277-296
    • Ruzmaikina, A.1
  • 35
    • 0343861172 scopus 로고    scopus 로고
    • A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge
    • Sinai Y., Soshnikov A. A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge. Funct. Anal. Appl. 1998, 32(2):114-131.
    • (1998) Funct. Anal. Appl. , vol.32 , Issue.2 , pp. 114-131
    • Sinai, Y.1    Soshnikov, A.2
  • 36
    • 70350418110 scopus 로고    scopus 로고
    • The Tracy-Widom law for some sparse random matrices
    • Sodin S. The Tracy-Widom law for some sparse random matrices. J. Stat. Phys. 2009, 136(5):834-841.
    • (2009) J. Stat. Phys. , vol.136 , Issue.5 , pp. 834-841
    • Sodin, S.1
  • 37
    • 77957911182 scopus 로고    scopus 로고
    • The spectral edge of some random band matrices
    • Sodin S. The spectral edge of some random band matrices. Ann. of Math. 2010, 172(3):2223-2251.
    • (2010) Ann. of Math. , vol.172 , Issue.3 , pp. 2223-2251
    • Sodin, S.1
  • 38
    • 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. 1999, 207(3):697-733.
    • (1999) Comm. Math. Phys. , vol.207 , Issue.3 , pp. 697-733
    • Soshnikov, A.1
  • 39
    • 4644351110 scopus 로고    scopus 로고
    • Poisson statistics for the largest eigenvalues of Wigner matrices with heavy tails
    • Soshnikov A. Poisson statistics for the largest eigenvalues of Wigner matrices with heavy tails. Electron. Commun. Probab. 2004, 9:82-91.
    • (2004) Electron. Commun. Probab. , vol.9 , pp. 82-91
    • Soshnikov, A.1
  • 40
    • 84855605232 scopus 로고    scopus 로고
    • Review article on random band matrices, in preparation.
    • T. Spencer, Review article on random band matrices, in preparation.
    • Spencer, T.1
  • 41
    • 79953112440 scopus 로고    scopus 로고
    • Random matrices: universality of the local eigenvalue statistics
    • Tao T., Vu V. Random matrices: universality of the local eigenvalue statistics. Acta Math. 2011, 206(1):127-204.
    • (2011) Acta Math. , vol.206 , Issue.1 , pp. 127-204
    • Tao, T.1    Vu, V.2
  • 44
    • 27644532196 scopus 로고
    • Level-spacing distributions and the Airy kernel
    • Tracy C., Widom H. Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 1994, 159:151-174.
    • (1994) Comm. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 45
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • Tracy C., Widom H. On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 1996, 177(3):727-754.
    • (1996) Comm. Math. Phys. , vol.177 , Issue.3 , pp. 727-754
    • Tracy, C.1    Widom, H.2
  • 46
    • 0000840166 scopus 로고
    • Characteristic vectors of bordered matrices with infinite dimensions
    • Wigner E. Characteristic vectors of bordered matrices with infinite dimensions. Ann. of Math. 1955, 62:548-564.
    • (1955) Ann. of Math. , vol.62 , pp. 548-564
    • Wigner, E.1


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