메뉴 건너뛰기




Volumn 28, Issue 3, 2000, Pages 1353-1370

The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities

Author keywords

Central limit theorem; Compact groups and; Kac Spitzer combinatorial lemma; Random matrices

Indexed keywords


EID: 0034214587     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1019160338     Document Type: Article
Times cited : (130)

References (39)
  • 1
    • 84874187337 scopus 로고
    • On sums of symmetrically dependent random variables
    • ANDERSEN, E. S. (1953). On sums of symmetrically dependent random variables. Skand. Aktuarietidskr. 36 123-138.
    • (1953) Skand. Aktuarietidskr. , vol.36 , pp. 123-138
    • Andersen, E.S.1
  • 2
    • 0002067901 scopus 로고
    • Note sur une relation les intégrales définies des produits des fonctions
    • ANDRÉIEF, C. (1883). Note sur une relation les intégrales définies des produits des fonctions. Mém. de la Soc. Sci. Bordeaux 2 1-14.
    • (1883) Mém. de la Soc. Sci. Bordeaux , vol.2 , pp. 1-14
    • Andréief, C.1
  • 3
    • 0040052023 scopus 로고    scopus 로고
    • Finite N fluctuation formulas for random matrices
    • BAKER, T. H. and FORRESTER, P. J. (1997). Finite N fluctuation formulas for random matrices. J. Statist. Phys. 88 1371-1385.
    • (1997) J. Statist. Phys. , vol.88 , pp. 1371-1385
    • Baker, T.H.1    Forrester, P.J.2
  • 4
    • 0031479723 scopus 로고    scopus 로고
    • Distribution functions for random variables for ensembles of positive Hermitian matrices
    • BASOR, E. (1997). Distribution functions for random variables for ensembles of positive Hermitian matrices. Comm. Math. Phys. 188 327-350.
    • (1997) Comm. Math. Phys. , vol.188 , pp. 327-350
    • Basor, E.1
  • 5
    • 0000765503 scopus 로고
    • Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols
    • BASOR, E. and WIDOM, H. (1983). Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols. J. Funct. Anal. 50 387-413.
    • (1983) J. Funct. Anal. , vol.50 , pp. 387-413
    • Basor, E.1    Widom, H.2
  • 6
    • 0002030459 scopus 로고
    • Combinatorial methods in fluctuation theory
    • BAXTER, G. (1963). Combinatorial methods in fluctuation theory. Z. Wahrsch. Verw. Gebiete 1 263-270.
    • (1963) Z. Wahrsch. Verw. Gebiete , vol.1 , pp. 263-270
    • Baxter, G.1
  • 7
    • 21844500668 scopus 로고
    • The onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators
    • BÖTTCHER, A. (1995). The Onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators. J. Statist. Phys. 78 575-588.
    • (1995) J. Statist. Phys. , vol.78 , pp. 575-588
    • Böttcher, A.1
  • 10
    • 0002542182 scopus 로고
    • Gaussian fluctuations in random matrices
    • COSTIN, O. and LEBOWITZ, J. (1995). Gaussian fluctuations in random matrices. Phys. Rev. Lett. 75 69-72.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 69-72
    • Costin, O.1    Lebowitz, J.2
  • 11
    • 84972538991 scopus 로고
    • The strong Szegö limit theorem
    • DEVINATZ, A. (1967). The strong Szegö limit theorem. Illinois J. Math. 11 160-175.
    • (1967) Illinois J. Math. , vol.11 , pp. 160-175
    • Devinatz, A.1
  • 13
    • 0001891773 scopus 로고
    • On the eigenvalues of random matrices
    • DIACONIS, P. and SHAHSHAHANI, M. (1994). On the eigenvalues of random matrices. J. Appl. Probab. 31A 49-62.
    • (1994) J. Appl. Probab. , vol.31 A , pp. 49-62
    • Diaconis, P.1    Shahshahani, M.2
  • 14
    • 0039430657 scopus 로고
    • Correlations between eigenvalues of a random matrix
    • DYSON, F. J. (1970). Correlations between eigenvalues of a random matrix. Comm. Math. Phys. 19 235-250.
    • (1970) Comm. Math. Phys. , vol.19 , pp. 235-250
    • Dyson, F.J.1
  • 15
    • 84949237115 scopus 로고
    • Toeplitz determinants, some applications, theorems and conjectures
    • FISHER, H. E. and HARTWING, R. E. (1968). Toeplitz determinants, some applications, theorems and conjectures. Adv. Chem. Phys. 15 333-353.
    • (1968) Adv. Chem. Phys. , vol.15 , pp. 333-353
    • Fisher, H.E.1    Hartwing, R.E.2
  • 17
    • 51249168980 scopus 로고
    • On a theorem of Szegö, Kac and Baxter
    • HIRSCHMAN, JR., I. I. (1965). On a theorem of Szegö, Kac and Baxter. J. d'Analyse Math. 14 225-234.
    • (1965) J. d'Analyse Math. , vol.14 , pp. 225-234
    • Hirschman I.I., Jr.1
  • 19
    • 0001677729 scopus 로고
    • On Szegö's asymptotic formula for Toeplitz determinants and generalizations
    • JOHANSSON, K. (1988). On Szegö's asymptotic formula for Toeplitz determinants and generalizations. Bull. Sci. Math. 112 257-304.
    • (1988) Bull. Sci. Math. , vol.112 , pp. 257-304
    • Johansson, K.1
  • 20
    • 0031525857 scopus 로고    scopus 로고
    • On random matrices from classical compact groups
    • JOHANSSON, K. (1997). On random matrices from classical compact groups. Ann. of Math. 145 519-545.
    • (1997) Ann. of Math. , vol.145 , pp. 519-545
    • Johansson, K.1
  • 21
    • 0001459956 scopus 로고    scopus 로고
    • On fluctuation of eigenvalues of random Hermitian matrices
    • JOHANSSON, K. (1998). On fluctuation of eigenvalues of random Hermitian matrices. Duke Math. J. 91 151-204.
    • (1998) Duke Math. J. , vol.91 , pp. 151-204
    • Johansson, K.1
  • 22
    • 84972538834 scopus 로고
    • Toeplitz matrices, translation kernels and a related problem in probability theory
    • KAC, M. (1954). Toeplitz matrices, translation kernels and a related problem in probability theory. Duke Math. J. 21 501-509.
    • (1954) Duke Math. J. , vol.21 , pp. 501-509
    • Kac, M.1
  • 24
    • 0030494613 scopus 로고    scopus 로고
    • Asymptotic properties of large random matrices with independent entries
    • KHORUNZHY, A., KHORUZHENKO, B. and PASTUR, L. (1996). Asymptotic properties of large random matrices with independent entries. J. Math. Phys. 37 5033-5059.
    • (1996) J. Math. Phys. , vol.37 , pp. 5033-5059
    • Khorunzhy, A.1    Khoruzhenko, B.2    Pastur, L.3
  • 27
    • 0000580673 scopus 로고    scopus 로고
    • Zeroes of principal L-functions and random matrix theory. A celebration of John F. Nash, Jr.
    • RUDNICK, Z. and SARNAK, P. (1996). Zeroes of principal L-functions and random matrix theory. A celebration of John F. Nash, Jr. Duke Math. J. 61 269-322.
    • (1996) Duke Math. J. , vol.61 , pp. 269-322
    • Rudnick, Z.1    Sarnak, P.2
  • 28
    • 0343861172 scopus 로고    scopus 로고
    • A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices
    • SINAI, YA and SOSHNIKOV, A. (1998). A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices. Funct. Anal. Appl. 32 114-131.
    • (1998) Funct. Anal. Appl. , vol.32 , pp. 114-131
    • Sinai, Y.A.1    Soshnikov, A.2
  • 29
    • 27144550468 scopus 로고    scopus 로고
    • Central limit theorem for traces of large random matrices with independent entries
    • SINAI, YA. and SOSHNIKOV, A. (1998). Central limit theorem for traces of large random matrices with independent entries. Bol. Soc. Brasil. Mat. 29 1-24.
    • (1998) Bol. Soc. Brasil. Mat. , vol.29 , pp. 1-24
    • Sinai, Ya.1    Soshnikov, A.2
  • 30
    • 0032285810 scopus 로고    scopus 로고
    • Level spacings distribution for large random matrices: Gaussian fluctuations
    • SOSHNIKOV, A. (1998). Level spacings distribution for large random matrices: Gaussian fluctuations. Ann. of Math. 148 573-617.
    • (1998) Ann. of Math. , vol.148 , pp. 573-617
    • Soshnikov, A.1
  • 31
    • 0002159288 scopus 로고    scopus 로고
    • Gaussian fluctuations in Airy, Bessel, sine and other determinantal random point fields
    • SOSHNIKOV, A. (1999). Gaussian fluctuations in Airy, Bessel, sine and other determinantal random point fields. J. Statist. Phys. 100. Available at http://xxx.lanl.gov/abs/ math/9907012.
    • (1999) J. Statist. Phys. , vol.100
    • Soshnikov, A.1
  • 32
    • 84967710276 scopus 로고
    • A combinatorial lemma and its applications to probability theory
    • SPITZER, F. (1956). A combinatorial lemma and its applications to probability theory. Trans. Amer. Math. Soc. 82 323-339.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 323-339
    • Spitzer, F.1
  • 33
    • 0001362231 scopus 로고
    • Interacting Brownian particles: A study of Dyson's model
    • (G. Papanicolau, ed.) Springer, New York
    • SPOHN, H. (1987). Interacting Brownian particles: A study of Dyson's model. In Hydrodynamic Behavior and Interacting Particle Systems (G. Papanicolau, ed.) Springer, New York.
    • (1987) Hydrodynamic Behavior and Interacting Particle Systems
    • Spohn, H.1
  • 34
    • 0001405026 scopus 로고
    • On certain Hermitian forms associated with the Fourier series of a positive functions
    • SZEGÖ, G. (1952). On certain Hermitian forms associated with the Fourier series of a positive functions. Comm. Seminaire Math, de l'Univ. de Lund, tome supplémentaire 228-237.
    • (1952) Comm. Seminaire Math, de l'Univ. de Lund, Tome Supplémentaire , pp. 228-237
    • Szegö, G.1
  • 35
    • 0032163852 scopus 로고    scopus 로고
    • Correlation functions, cluster functions, and spacing distributions for random matrices
    • TRACY, C. A. and WIDOM, H. (1998). Correlation functions, cluster functions, and spacing distributions for random matrices. J. Statist. Phys. 92 809-835.
    • (1998) J. Statist. Phys. , vol.92 , pp. 809-835
    • Tracy, C.A.1    Widom, H.2
  • 37
    • 0000920179 scopus 로고
    • Toeplitz determinants with single generating function
    • WIDOM, H. (1973). Toeplitz determinants with single generating function. Amer. J. Math. 95 333-383.
    • (1973) Amer. J. Math. , vol.95 , pp. 333-383
    • Widom, H.1
  • 38
    • 0041658306 scopus 로고
    • Asymptotic behaviour of block Toeplitz matrices and determinants I, II
    • WIDOM, H. (1973) (1976). Asymptotic behaviour of block Toeplitz matrices and determinants I, II. Adv. Math. 13 284-322, 21 1-29.
    • (1973) Adv. Math. , vol.13-21 , pp. 284-322
    • Widom, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.