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Volumn 40, Issue 3, 2012, Pages 1737-1763

Edge universality of correlation matrices

Author keywords

Correlation matrix; Covariance matrix; Marcenko Pastur law; Universality

Indexed keywords


EID: 84872085835     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AOS1022     Document Type: Article
Times cited : (50)

References (27)
  • 2
    • 33947520702 scopus 로고    scopus 로고
    • A generalization of the lindeberg principle
    • MR2294976
    • CHATTERJEE, S. (2006). A generalization of the Lindeberg principle. Ann. Probab. 34 2061-2076. MR2294976
    • (2006) Ann. Probab. , vol.34 , pp. 2061-2076
    • Chatterjee, S.1
  • 6
    • 77949568197 scopus 로고    scopus 로고
    • Semicircle law on short scales and delocalization of eigenvectors for wigner random matrices
    • MR2537522
    • ERDO S, L., SCHLEIN, B. and YAU, H.-T. (2009). Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Ann. Probab. 37 815-852. MR2537522
    • (2009) Ann. Probab. , vol.37 , pp. 815-852
    • Erdo, S.L.1    Schlein, B.2    Yau, H.-T.3
  • 7
    • 61549110549 scopus 로고    scopus 로고
    • Local semicircle law and complete delocalization for wigner random matrices
    • MR2481753
    • ERDO S, L., SCHLEIN, B. and YAU, H.-T. (2009). Local semicircle law and complete delocalization for Wigner random matrices. Comm. Math. Phys. 287 641-655. MR2481753
    • (2009) Comm. Math. Phys. , vol.287 , pp. 641-655
    • Erdo, S.L.1    Schlein, B.2    Yau, H.-T.3
  • 8
    • 77953168459 scopus 로고    scopus 로고
    • Wegner estimate and level repulsion for wigner random matrices
    • MR2587574
    • ERDO S, L., SCHLEIN, B. and YAU, H.-T. (2010). Wegner estimate and level repulsion for Wigner random matrices. Int. Math. Res. Not. IMRN 3 436-479. MR2587574
    • (2010) Int. Math. Res. Not. IMRN , vol.3 , pp. 436-479
    • Erdo, S.L.1    Schlein, B.2    Yau, H.-T.3
  • 9
    • 79959217986 scopus 로고    scopus 로고
    • Universality of random matrices and local relaxation flow
    • MR2810797
    • ERDO S, L., SCHLEIN, B. and YAU, H.-T. (2011). Universality of random matrices and local relaxation flow. Invent. Math. 185 75-119. MR2810797
    • (2011) Invent. Math. , vol.185 , pp. 75-119
    • Erdo, S.L.1    Schlein, B.2    Yau, H.-T.3
  • 10
    • 84856298820 scopus 로고    scopus 로고
    • The local relaxation flow approach to universality of the local statistics for random matrices
    • MR2919197
    • ERDO S, L., SCHLEIN, B., YAU, H.-T. and YIN, J. (2012). The local relaxation flow approach to universality of the local statistics for random matrices. Ann. Inst. Henri Poincaré Probab. Stat. 48 1-46. MR2919197
    • (2012) Ann. Inst. Henri Poincaré Probab. Stat. , vol.48 , pp. 1-46
    • Erdo, S.L.1    Schlein, B.2    Yau, H.-T.3    Yin, J.4
  • 11
    • 84855612683 scopus 로고    scopus 로고
    • Universality for generalized wigner matrices with bernoulli distribution
    • MR2847916
    • ERDO S, L.,YAU, H.-T. andYIN, J. (2011). Universality for generalized Wigner matrices with Bernoulli distribution. J. Comb. 2 15-81. MR2847916
    • (2011) J. Comb. , vol.2 , pp. 15-81
    • Erdo, S.L.1    Yau, H.-T.2    Yin, J.3
  • 13
    • 84055178439 scopus 로고    scopus 로고
    • Rigidity of eigenvalues of generalized wigner matrices
    • MR2871147
    • ERDO S, L., YAU, H.-T. and YIN, J. (2012). Rigidity of eigenvalues of generalized Wigner matrices. Adv. Math. 229 1435-1515. MR2871147
    • (2012) Adv. Math. , vol.229 , pp. 1435-1515
    • Erdo, S.L.1    Yau, H.-T.2    Yin, J.3
  • 14
    • 77952877492 scopus 로고    scopus 로고
    • A universality result for the smallest eigenvalues of certain sample covariance matrices
    • MR2647136
    • FELDHEIM, O. N. and SODIN, S. (2010). A universality result for the smallest eigenvalues of certain sample covariance matrices. Geom. Funct. Anal. 20 88-123. MR2647136
    • (2010) Geom. Funct. Anal. , vol.20 , pp. 88-123
    • Feldheim, O.N.1    Sodin, S.2
  • 15
    • 47849095724 scopus 로고    scopus 로고
    • The limiting distributions of eigenvalues of sample correlation matrices
    • MR2082906
    • JIANG, T. (2004). The limiting distributions of eigenvalues of sample correlation matrices. Sankhȳa 66 35-48. MR2082906
    • (2004) Sankhȳa , vol.66 , pp. 35-48
    • Jiang, T.1
  • 16
    • 84856276225 scopus 로고    scopus 로고
    • Universality for certain hermitian wigner matrices under weak moment conditions
    • MR2919198
    • JOHANSSON, K. (2012). Universality for certain Hermitian Wigner matrices under weak moment conditions. Ann. Inst. Henri Poincaré Probab. Stat. 48 47-79. MR2919198
    • (2012) Ann. Inst. Henri Poincaré Probab. Stat. , vol.48 , pp. 47-79
    • Johansson, K.1
  • 17
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • MR1863961
    • JOHNSTONE, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295-327. MR1863961
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 18
    • 79961039847 scopus 로고    scopus 로고
    • High dimensional statistical inference and random matrices
    • Eur Math Soc Zürich MR2334195
    • JOHNSTONE, I. M. (2007). High dimensional statistical inference and random matrices. In International Congress of Mathematicians. Vol. I 307-333. Eur. Math. Soc., Zürich. MR2334195
    • (2007) International Congress of Mathematicians. , vol.1 , pp. 307-333
    • Johnstone, I.M.1
  • 19
    • 62349134314 scopus 로고    scopus 로고
    • Multivariate analysis and jacobi ensembles: Largest eigenvalue, tracy-widom limits and rates of convergence
    • MR2485010
    • JOHNSTONE, I. M. (2008). Multivariate analysis and Jacobi ensembles: Largest eigenvalue, Tracy-Widom limits and rates of convergence. Ann. Statist. 36 2638-2716. MR2485010
    • (2008) Ann. Statist. , vol.36 , pp. 2638-2716
    • Johnstone, I.M.1
  • 22
    • 0000263239 scopus 로고
    • Distribution of eigenvalues in certain sets of random matrices
    • MR0208649
    • MARC ENKO, V. A. and PASTUR, L. A. (1967). Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N.S.) 72 507-536. MR0208649
    • (1967) Mat. Sb. (N.S.) , vol.72 , pp. 507-536
    • Marc Enko, V.A.1    Pastur, L.A.2
  • 23
    • 59449098080 scopus 로고    scopus 로고
    • Universality results for the largest eigenvalues of some sample covariance matrix ensembles
    • MR2475670
    • PÉCHÉ, S. (2009). Universality results for the largest eigenvalues of some sample covariance matrix ensembles. Probab. Theory Related Fields 143 481-516. MR2475670
    • (2009) Probab. Theory Related Fields , vol.143 , pp. 481-516
    • Péché, S.1
  • 25
    • 0141450345 scopus 로고    scopus 로고
    • A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
    • Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays. MR1933444
    • SOSHNIKOV, A. (2002). A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices. J. Stat. Phys. 108 1033-1056. Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays. MR1933444
    • (2002) J. Stat. Phys. , vol.108 , pp. 1033-1056
    • Soshnikov, A.1
  • 26
    • 77954624704 scopus 로고    scopus 로고
    • Random matrices: Universality of local eigenvalue statistics up to the edge
    • MR2669449
    • TAO, T. and VU, V. (2010). Random matrices: Universality of local eigenvalue statistics up to the edge. Comm. Math. Phys. 298 549-572. MR2669449
    • (2010) Comm. Math. Phys. , vol.298 , pp. 549-572
    • Tao, T.1    Vu, V.2
  • 27
    • 84863108484 scopus 로고    scopus 로고
    • Random covariance matrices: Universality of local statistics of eigenvalues
    • TAO, T. and VU, V. (2012). Random covariance matrices: Universality of local statistics of eigenvalues. Ann. Probab. 40 1285-1315.
    • (2012) Ann. Probab. , vol.40 , pp. 1285-1315
    • Tao, T.1    Vu, V.2


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