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Volumn 161, Issue 3, 2005, Pages 1319-1422

Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes

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EID: 21644449975     PISSN: 0003486X     EISSN: 0003486X     Source Type: Journal    
DOI: 10.4007/annals.2005.161.1319     Document Type: Article
Times cited : (105)

References (69)
  • 1
    • 21844516576 scopus 로고
    • Correlations in two-component log-gas systems
    • [AF]
    • [AF] A. ALASTUEY and P. J. FORRESTER, Correlations in two-component log-gas systems, J. Statist. Phys. 81 (1995), 579-627.
    • (1995) J. Statist. Phys. , vol.81 , pp. 579-627
    • Alastuey, A.1    Forrester, P.J.2
  • 2
    • 0001929478 scopus 로고
    • An integral of Ramanujan and orthogonal polynomials
    • [As]
    • [As] R. ASKEY, An integral of Ramanujan and orthogonal polynomials, J. Indian Math. Soc. 51 (1987), 27-36.
    • (1987) J. Indian Math. Soc. , vol.51 , pp. 27-36
    • Askey, R.1
  • 3
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • [BDJ]; math/9810105.
    • [BDJ] J. Baik, P. Deift, and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999), 1119-1178; math/9810105.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 5
    • 84990617857 scopus 로고
    • Scattering and inverse scattering for first order systems
    • [BC]
    • [BC] R. BEALS and R. R. COIFMAN, Scattering and inverse scattering for first order systems Comm. Pure Appl. Math. 37 (1984), 39-90.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 39-90
    • Beals, R.1    Coifman, R.R.2
  • 7
    • 0348014381 scopus 로고    scopus 로고
    • Characters of symmetric groups and correlation functions of point processes
    • [B1]
    • [B1] A. BORODIN, Characters of symmetric groups and correlation functions of point processes, Funct. Anal. Appl. 34 (2000), 10-23.
    • (2000) Funct. Anal. Appl. , vol.34 , pp. 10-23
    • Borodin, A.1
  • 8
    • 0037727539 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite symmetric group, and the Whittaker kernel
    • [B2]
    • [B2] _, Harmonic analysis on the infinite symmetric group, and the Whittaker kernel, St. Petersburg Math. J. 12 (2001), 733-759.
    • (2001) St. Petersburg Math. J. , vol.12 , pp. 733-759
  • 9
    • 0346737796 scopus 로고    scopus 로고
    • Riemann-Hilbert problem and the discrete Bessel kernel
    • [B3]; math/9912093
    • [B3] _, Riemann-Hilbert problem and the discrete Bessel kernel, Internat. Math. Res. Notices 2000, no. 9, 467-494; math/9912093.
    • (2000) Internat. Math. Res. Notices , vol.9 , pp. 467-494
  • 10
    • 0032576497 scopus 로고    scopus 로고
    • Biorthogonal ensembles
    • [B4]; math/9804027
    • [B4] _, Biorthogonal ensembles, Nuclear Phys. B 536 (1998), 704-732; math/9804027.
    • (1998) Nuclear Phys. B , vol.536 , pp. 704-732
  • 11
    • 0036390386 scopus 로고    scopus 로고
    • Duality of orthogonal polynomials on a finite set
    • [B5]; math/0101125
    • [B5] _, Duality of orthogonal polynomials on a finite set J. Statist. Phys. 109 (2002), 1109-1120; math/0101125.
    • (2002) J. Statist. Phys. , vol.109 , pp. 1109-1120
  • 12
    • 0036329601 scopus 로고    scopus 로고
    • Fredholm determinants, Jimbo-Miwa-Ueno τ-functions, and representation theory
    • [BD]; math/0111007
    • [BD] A. BORODIN and P. DEIFT, Fredholm determinants, Jimbo-Miwa-Ueno τ-functions, and representation theory, Comm. Pure Appl. Math. 55 (2002), 1160-1230; math/0111007.
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 1160-1230
    • Borodin, A.1    Deift, P.2
  • 13
    • 0034390399 scopus 로고    scopus 로고
    • Asymptotics of Plancherel measures for symmetric groups
    • [BOO]; math/9905032
    • [BOO] A. BORODIN, A. OKOUNKOV, and G. OLSHANSKI, Asymptotics of Plancherel measures for symmetric groups, J. Amer. Math. Soc. 13 (2000), 481-515; math/9905032.
    • (2000) J. Amer. Math. Soc. , vol.13 , pp. 481-515
    • Borodin, A.1    Okounkov, A.2    Olshanski, G.3
  • 14
    • 0032216968 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group
    • [BO1]; math/9810015
    • [BO1] A. BORODIN and G. OLSHANSKI, Point processes and the infinite symmetric group, Math. Res. Lett. 5 (1998), 799-816; math/9810015.
    • (1998) Math. Res. Lett. , vol.5 , pp. 799-816
    • Borodin, A.1    Olshanski, G.2
  • 15
    • 0034349003 scopus 로고    scopus 로고
    • Distributions on partitions, point processes and the hypergeometric kernel
    • [BO2]; math/9904010
    • [BO2] _, Distributions on partitions, point processes and the hypergeometric kernel, Comm. Math. Phys. 211 (2000), 335-358; math/9904010.
    • (2000) Comm. Math. Phys. , vol.211 , pp. 335-358
  • 16
    • 0012593006 scopus 로고    scopus 로고
    • Z-Measures on partitions, Robinson-Schensted-Knuth correspondence, and β = 2 random matrix ensembles
    • [BO3], Random Matrix Models and Their Applications (P. M. Bleher and A. R. Its, eds.),math/9905189
    • [BO3] _, z-Measures on partitions, Robinson-Schensted-Knuth correspondence, and β = 2 random matrix ensembles, in Random Matrix Models and Their Applications (P. M. Bleher and A. R. Its, eds.), Math. Sci. Res. Inst. Publ. 40 (2001), 71-94; math/9905189.
    • (2001) Math. Sci. Res. Inst. Publ. , vol.40 , pp. 71-94
  • 17
    • 0035537377 scopus 로고    scopus 로고
    • Infinite random matrices and ergodic measures
    • [BO4]; math-ph/0010015
    • [BO4] _, Infinite random matrices and ergodic measures Comm. Math. Phys. 203 (2001), 87-123; math-ph/0010015.
    • (2001) Comm. Math. Phys. , vol.203 , pp. 87-123
  • 18
    • 0010961303 scopus 로고
    • Infinite traces of AF-algebras and characters of U(∞)
    • [Boy]
    • [Boy] R. P. BOYER, Infinite traces of AF-algebras and characters of U(∞), J. Operator Theory 9 (1983), 205-236.
    • (1983) J. Operator Theory , vol.9 , pp. 205-236
    • Boyer, R.P.1
  • 19
    • 0002720913 scopus 로고
    • On the two-dimensional Coulomb gas
    • [CJ1]
    • [CJ1] F. CORNU and B. JANCOVICI, On the two-dimensional Coulomb gas, J. Statist. Phys. 49 (1987), 33-56.
    • (1987) J. Statist. Phys. , vol.49 , pp. 33-56
    • Cornu, F.1    Jancovici, B.2
  • 20
    • 0001305432 scopus 로고
    • The electrical double layer: A solvable model
    • [CJ2]
    • [CJ2] _, The electrical double layer: a solvable model J. Chem. Phys. 90 (1989), 2444.
    • (1989) J. Chem. Phys. , vol.90 , pp. 2444
  • 22
    • 0001946143 scopus 로고    scopus 로고
    • Integrable operators
    • [De], Differential Operators and Spectral Theory: M. Sh. Birman's 70th anniversary collection, V. Buslaev, M. Solomyak, and D. Yafaev, eds., A. M. S., Providence, RI
    • [De] P. DEIFT, Integrable operators, in Differential Operators and Spectral Theory: M. Sh. Birman's 70th anniversary collection, V. Buslaev, M. Solomyak, and D. Yafaev, eds., Amer. Math. Soc. Transl. 189 A. M. S., Providence, RI, 1999.
    • (1999) Amer. Math. Soc. Transl. , vol.189
    • Deift, P.1
  • 23
    • 35549006412 scopus 로고
    • Statistical theory of the energy levels of complex systems. I, II, III
    • [Dy]
    • [Dy] F. J. DYSON, Statistical theory of the energy levels of complex systems. I, II, III, J. Mathematical Phys. 3 (1962), 140-156, 157-165, 166-175.
    • (1962) J. Mathematical Phys. , vol.3 , pp. 140-156
    • Dyson, F.J.1
  • 24
    • 84966224610 scopus 로고
    • On the generating function of a doubly-infinite, totally positive sequence
    • [Ed]
    • [Ed] A. EDREI, On the generating function of a doubly-infinite, totally positive sequence, Trans. Amer. Math. Soc. 74 (1953), 367-383.
    • (1953) Trans. Amer. Math. Soc. , vol.74 , pp. 367-383
    • Edrei, A.1
  • 25
    • 0008473958 scopus 로고
    • [Er] Mc Graw-Hill Book Co., Inc., New York
    • [Er] A. ERDELYI (ED.), Higher Transcendental Functions, Vols, 1, 2 Mc Graw-Hill Book Co., Inc., New York, 1953.
    • (1953) Higher Transcendental Functions , vol.1-2
    • Erdelyi, A.1
  • 26
    • 0002377230 scopus 로고
    • Positive and negative charged rods alternating along a line: Exact results
    • [F1]
    • [F1] P. J. FORRESTER, Positive and negative charged rods alternating along a line: exact results, J. Statist. Phys. 45 (1986), 153-169.
    • (1986) J. Statist. Phys. , vol.45 , pp. 153-169
    • Forrester, P.J.1
  • 27
    • 0000443356 scopus 로고
    • Solvable isotherms for a two-component system of charged rods on a line
    • [F2]
    • [F2] _, Solvable isotherms for a two-component system of charged rods on a line, J. Statist. Phys. 51 (1988), 457-479.
    • (1988) J. Statist. Phys. , vol.51 , pp. 457-479
  • 28
    • 0002100322 scopus 로고
    • Exact results for correlations in a two-component log-gas
    • [F3]
    • [F3] _, Exact results for correlations in a two-component log-gas, J. Statist. Phys. 54 (1989), 57-79.
    • (1989) J. Statist. Phys. , vol.54 , pp. 57-79
  • 29
    • 0022101562 scopus 로고
    • L'isotherme critique d'un plasma sur réseau (β = 2, d = 2, n = 2)
    • [G]
    • [G] M. GAUDIN, L'isotherme critique d'un plasma sur réseau (β = 2, d = 2, n = 2), J. Physique 46 (1985), 1027-1042.
    • (1985) J. Physique , vol.46 , pp. 1027-1042
    • Gaudin, M.1
  • 32
    • 0035626398 scopus 로고    scopus 로고
    • Discrete orthogonal polynomial ensembles and the Plancherel measure
    • [J]; math/9906120
    • [J] K. JOHANSSON, Discrete orthogonal polynomial ensembles and the Plancherel measure, Ann. of Math. 153 (2001), 259-296; math/9906120.
    • (2001) Ann. of Math. , vol.153 , pp. 259-296
    • Johansson, K.1
  • 33
    • 30444442190 scopus 로고    scopus 로고
    • A multidimensional hypergeometric distribution and characters of the unitary group
    • [Ke] Russian
    • [Ke] S. V. KEROV, A multidimensional hypergeometric distribution and characters of the unitary group, Zapiski Nauchn. Semin. POMI 31 (2003), 35-91 (Russian);
    • (2003) Zapiski Nauchn. Semin. POMI , vol.31 , pp. 35-91
    • Kerov, S.V.1
  • 34
    • 30444443525 scopus 로고    scopus 로고
    • English translation to appear in (New York)
    • English translation to appear in J. Math. Sciences (New York).
    • J. Math. Sciences
  • 35
  • 36
    • 0001656032 scopus 로고
    • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
    • [KOV]
    • [KOV] S. KEROV, G. OLSHANSKI, and A. VERSHIK, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation, C. R. Acad. Sci. Paris, Sér. I 316 (1993), 773-778;
    • (1993) C. R. Acad. Sci. Paris, Sér. I , vol.316 , pp. 773-778
    • Kerov, S.1    Olshanski, G.2    Vershik, A.3
  • 37
    • 11144268918 scopus 로고    scopus 로고
    • detailed version in Invent. Math. 158 (2004), 551-642.
    • (2004) Invent. Math. , vol.158 , pp. 551-642
  • 39
    • 0002516103 scopus 로고
    • Correlation functions and the uniqueness of the state in classical statistical mechanics
    • [Len]
    • [Len] A. LENARD, Correlation functions and the uniqueness of the state in classical statistical mechanics, Comm. Math. Phys. 30 (1973), 35-44.
    • (1973) Comm. Math. Phys. , vol.30 , pp. 35-44
    • Lenard, A.1
  • 40
    • 84994184315 scopus 로고    scopus 로고
    • Unendliche und endliche Orthogonalsysteme von Continuous Hahnpolynomen
    • [Les1]
    • [Les1] P. A. LESKY, Unendliche und endliche Orthogonalsysteme von Continuous Hahnpolynomen, Results Math. 31 (1997), 127-135.
    • (1997) Results Math. , vol.31 , pp. 127-135
    • Lesky, P.A.1
  • 44
    • 0000817750 scopus 로고
    • Correlation functions of random matrix ensembles related to classical orthogonal polynomials
    • [NW]
    • [NW] T. NAGAO and M. WADATI, Correlation functions of random matrix ensembles related to classical orthogonal polynomials, J. Phys. Soc. Japan 60 (1991), 3298-3322.
    • (1991) J. Phys. Soc. Japan , vol.60 , pp. 3298-3322
    • Nagao, T.1    Wadati, M.2
  • 45
    • 0037104083 scopus 로고    scopus 로고
    • Hua type integrals over unitary groups and over projective limits of unitary groups
    • [Ner]
    • [Ner] YU. A. NERETIN, Hua type integrals over unitary groups and over projective limits of unitary groups, Duke Math. J. 114 (2002), 239-266.
    • (2002) Duke Math. J. , vol.114 , pp. 239-266
    • Neretin, Yu.A.1
  • 48
    • 1842788768 scopus 로고    scopus 로고
    • Asymptotics of Jack polynomials as the number of variables goes to infinity
    • [OkOl]
    • [OkOl] A. OKOUNKOV and G. OLSHANSKI, Asymptotics of Jack polynomials as the number of variables goes to infinity, Internat. Math. Res. Notices 1998, no. 13, 641-682.
    • (1998) Internat. Math. Res. Notices , vol.13 , pp. 641-682
    • Okounkov, A.1    Olshanski, G.2
  • 49
    • 0012360416 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • [Ol1]
    • [Ol1] G. OLSHANSKI, Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe, Soviet Math. Dokl. 27 (1983), 290-294.
    • (1983) Soviet Math. Dokl. , vol.27 , pp. 290-294
    • Olshanski, G.1
  • 50
    • 0001471212 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • [Ol2], Representation of Lie Groups and Related Topics, (A. Vershik and D. Zhelobenko, eds.), Gordon and Breach Science Publishers, New York
    • [Ol2] _, Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe, in Representation of Lie Groups and Related Topics, (A. Vershik and D. Zhelobenko, eds.), Advanced Studies in Contemporary Math. 7, Gordon and Breach Science Publishers, New York, 1990, pp. 269-463.
    • (1990) Advanced Studies in Contemporary Math. , vol.7 , pp. 269-463
  • 51
    • 0346343169 scopus 로고    scopus 로고
    • The problem of harmonic analysis on the infinite-dimensional unitary group
    • [Ol3]; math/0109193
    • [Ol3] _, The problem of harmonic analysis on the infinite-dimensional unitary group, J. Funct. Anal. 205 (2003), 464-524; math/0109193.
    • (2003) J. Funct. Anal. , vol.205 , pp. 464-524
  • 52
    • 0000236195 scopus 로고    scopus 로고
    • Ergodic unitarily invariant measures on the space of infinite Hermitian matrices
    • [OV], Contemp. Mathematical Physics (R. L. Dobrushin, R. A. Minlos, M. A. Shubin, and A. M. Vershik, eds.), A. M. S., Providence, R.I.
    • [OV] G. OLSHANSKI and A. VERSHIK, Ergodic unitarily invariant measures on the space of infinite Hermitian matrices, Contemp. Mathematical Physics (R. L. Dobrushin, R. A. Minlos, M. A. Shubin, and A. M. Vershik, eds.), Amer. Math. Soc. Transl. 175, 137-175, A. M. S., Providence, R.I., 1996.
    • (1996) Amer. Math. Soc. Transl. , vol.175 , pp. 137-175
    • Olshanski, G.1    Vershik, A.2
  • 53
    • 11144301672 scopus 로고    scopus 로고
    • Point processes related to the infinite symmetric group
    • [P.I], The Orbit Method in Geometry and Physics (Marseille, 2000), Birkhauser, Boston, math/9804086
    • [P.I] G. OLSHANSKI, Point processes related to the infinite symmetric group, in The Orbit Method in Geometry and Physics (Marseille, 2000), Prog. Math. 213 (2003), Birkhauser, Boston, 349-393; math/9804086.
    • (2003) Prog. Math. , vol.213 , pp. 349-393
    • Olshanski, G.1
  • 58
    • 0000249694 scopus 로고
    • Measures on infinite dimensional Grassmann manifold
    • [Pi1]
    • [Pi1] D. PICKRELL, Measures on infinite dimensional Grassmann manifold, J. Funct. Anal. 70 (1987), 323-356.
    • (1987) J. Funct. Anal. , vol.70 , pp. 323-356
    • Pickrell, D.1
  • 59
    • 84974000797 scopus 로고
    • Mackey analysis of infinite classical motion groups
    • [Pi2]
    • [Pi2] _, Mackey analysis of infinite classical motion groups, Pacific J. Math. 150 (1991), 139-166.
    • (1991) Pacific J. Math. , vol.150 , pp. 139-166
  • 61
    • 0034556390 scopus 로고    scopus 로고
    • Determinantal random point fields
    • [So]; math/0002099
    • [So] A. SOSHNIKOV, Determinantal random point fields, Russian Math. Surveys 55 (2000), 923-975; math/0002099.
    • (2000) Russian Math. Surveys , vol.55 , pp. 923-975
    • Soshnikov, A.1
  • 62
    • 0002043076 scopus 로고
    • Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
    • [Th]
    • [Th] E. THOMA, Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe, Math. Z. 85 (1964), 40-61.
    • (1964) Math. Z. , vol.85 , pp. 40-61
    • Thoma, E.1
  • 63
    • 0001683904 scopus 로고    scopus 로고
    • Universality of the distribution functions of random matrix theory
    • [TW], Integrable Systems: From Classical to Quantum (Montréal, QC, 1999), A. M. S., Providence, RI, solv-int/9901003
    • [TW] C. A. TRACY and H. WIDOM, Universality of the distribution functions of random matrix theory, in Integrable Systems: From Classical to Quantum (Montréal, QC, 1999) CRM Proc. Lecture Notes 26, 251-264, A. M. S., Providence, RI, 2000; solv-int/9901003.
    • (2000) CRM Proc. Lecture Notes , vol.26 , pp. 251-264
    • Tracy, C.A.1    Widom, H.2
  • 64
    • 34250241244 scopus 로고
    • Asymptotic theory of characters of the symmetric group
    • [VK1]
    • [VK1] A. M. VERSHIK and S. V. KEROV, Asymptotic theory of characters of the symmetric group, Funct. Anal. Appl. 15 (1981), 246-255.
    • (1981) Funct. Anal. Appl. , vol.15 , pp. 246-255
    • Vershik, A.M.1    Kerov, S.V.2
  • 65
    • 0000724260 scopus 로고
    • Characters and factor-representations of the infinite unitary group
    • [VK2]
    • [VK2] _, Characters and factor-representations of the infinite unitary group, Soviet Math. Dokl. 26 (1982), 570-574.
    • (1982) Soviet Math. Dokl. , vol.26 , pp. 570-574
  • 69
    • 30444444449 scopus 로고
    • English translation: A. M. S., Providence, RI
    • English translation: Transi. Math. Monographs 40, A. M. S., Providence, RI, 1973.
    • (1973) Transi. Math. Monographs , vol.40


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