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Volumn 16, Issue , 2011, Pages 2375-2405

Stein’s method and the multivariate CLT for traces of powers on the classical compact groups

Author keywords

Compact Lie groups; Exchangeable pairs; Haar measure; Heat kernel; Normal approximation; Power sum symmetric polynomials; Random matrices; Stein s method; Traces of powers

Indexed keywords


EID: 83255181625     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v16-960     Document Type: Article
Times cited : (34)

References (19)
  • 1
    • 77049111151 scopus 로고    scopus 로고
    • Multivariate normal approximation using exchangeable pairs
    • S. Chatterjee and E. Meckes. Multivariate normal approximation using exchangeable pairs. ALEALat. Am. J. Probab. Math. Stat., 4:257-283, 2008.
    • (2008) Alealat. Am. J. Probab. Math. Stat. , vol.4 , pp. 257-283
    • Chatterjee, S.1    Meckes, E.2
  • 3
    • 0001891773 scopus 로고
    • On the eigenvalues of random matrices
    • P Diaconis and M. Shahshahani. On the eigenvalues of random matrices. J. Appl. Probab., 31A:49-62, 1994.
    • (1994) J. Appl. Probab. , vol.31A , pp. 49-62
    • Diaconis, P.1    Shahshahani, M.2
  • 5
    • 33750620993 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI, 2000. Integral geometry, invariant differential operators, and spherical functions, Corrected reprint of the 1984 original
    • S. Helgason. Groups and geometric analysis, volume 83 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2000. Integral geometry, invariant differential operators, and spherical functions, Corrected reprint of the 1984 original.
    • Groups and Geometric Analysis, Volume 83 of Mathematical Surveys and Monographs.
    • Helgason, S.1
  • 6
    • 0037471288 scopus 로고    scopus 로고
    • Mock-Gaussian behaviour for linear statistics of classical compact groups
    • Random matrix theory
    • C. P Hughes and Z. Rudnick. Mock-Gaussian behaviour for linear statistics of classical compact groups. J. Phys. A, 36(12):2919-2932, 2003. Random matrix theory.
    • (2003) J. Phys. A , vol.36 , Issue.12 , pp. 2919-2932
    • Hughes, C.P.1    Rudnick, Z.2
  • 8
    • 0031525857 scopus 로고    scopus 로고
    • On random matrices from the compact classical groups
    • K. Johansson. On random matrices from the compact classical groups. Ann. Of Math. (2), 145(3):519-545, 1997.
    • (1997) Ann. Of Math. , vol.145 , Issue.2-3 , pp. 519-545
    • Johansson, K.1
  • 9
    • 41049103044 scopus 로고    scopus 로고
    • Schur-Weyl duality and the heat kernel measure on the unitary group
    • T. Lévy. Schur-Weyl duality and the heat kernel measure on the unitary group. Adv. Math., 218(2):537-575, 2008.
    • (2008) Adv. Math. , vol.218 , Issue.2 , pp. 537-575
    • Lévy, T.1
  • 10
    • 79957949749 scopus 로고    scopus 로고
    • On Stein’s method for multivariate normal approximation
    • IMS
    • E. Meckes. On Stein’s method for multivariate normal approximation. In High dimensional probability V: The Luminy volume, pages 153-158. IMS, 2009.
    • (2009) High Dimensional Probability V: The Luminy Volume , pp. 153-158
    • Meckes, E.1
  • 11
    • 11244278766 scopus 로고    scopus 로고
    • On the moments of traces of matrices of classical groups
    • L. Pastur and V Vasilchuk. On the moments of traces of matrices of classical groups. Comm. Math. Phys., 252(1-3):149-166, 2004.
    • (2004) Comm. Math. Phys. , vol.252 , Issue.1-3 , pp. 149-166
    • Pastur, L.1    Vasilchuk, V.2
  • 12
    • 0042732874 scopus 로고    scopus 로고
    • Combinatorial properties of Brownian motion on the compact classical groups
    • E. M. Rains. Combinatorial properties of Brownian motion on the compact classical groups. J. Theoret. Probab., 10(3):659-679, 1997.
    • (1997) J. Theoret. Probab. , vol.10 , Issue.3 , pp. 659-679
    • Rains, E.M.1
  • 13
    • 0031260684 scopus 로고    scopus 로고
    • On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics
    • Y. Rinott and V. Rotar. On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics. Ann. Appl. Probab., 7(4):1080-1105, 1997.
    • (1997) Ann. Appl. Probab. , vol.7 , Issue.4 , pp. 1080-1105
    • Rinott, Y.1    Rotar, V.2
  • 14
    • 77049095137 scopus 로고    scopus 로고
    • Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition
    • G. Reinert and A. Rollin. Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition. Ann. Probab., 37(6):2150-2173, 2009.
    • (2009) Ann. Probab. , vol.37 , Issue.6 , pp. 2150-2173
    • Reinert, G.1    Rollin, A.2
  • 15
    • 0001964876 scopus 로고
    • Topics in harmonic analysis related to the Littlewood-Paley theory
    • Princeton University Press, Princeton, N.J
    • E. M. Stein. Topics in harmonic analysis related to the Littlewood-Paley theory. Annals of Mathematics Studies, No. 63. Princeton University Press, Princeton, N.J., 1970.
    • (1970) Annals of Mathematics Studies , Issue.63
    • Stein, E.M.1
  • 19
    • 32944482188 scopus 로고    scopus 로고
    • On the Diaconis-Shahshahani method in random matrix theory
    • M. Stolz. On the Diaconis-Shahshahani method in random matrix theory. J. Algebraic Combin., 22(4):471-491, 2005.
    • (2005) J. Algebraic Combin. , vol.22 , Issue.4 , pp. 471-491
    • Stolz, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.