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Volumn , Issue 276, 2002, Pages 411-433

Random matrices and permutations, matrix integrals and integrable systems

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EID: 33747129478     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Review
Times cited : (2)

References (41)
  • 1
    • 33747118052 scopus 로고    scopus 로고
    • Symmetric random matrices and the Pfaff Lattice
    • to appear sept (solv-int/9903009) and The Hermitian, symmetric and symplectic ensembles and PDE's (math. -phys./009001)
    • M. ADLER and P. VAN MOERBEKE: Symmetric random matrices and the Pfaff Lattice, to appear in: Annals of Mathematics, sept 2000 (solv-int/9903009) and The Hermitian, symmetric and symplectic ensembles and PDE's (math. -phys./009001).
    • (2000) Annals of Mathematics
    • Adler, M.1    Van Moerbeke, P.2
  • 2
    • 0033439997 scopus 로고    scopus 로고
    • The spectrum of coupled random matrices
    • M. ADLER and P. VAN MOERBEKE: The spectrum of coupled random matrices, Annals of Mathematics, 149, 921-976 (1999).
    • (1999) Annals of Mathematics , vol.149 , pp. 921-976
    • Adler, M.1    Van Moerbeke, P.2
  • 3
    • 33747101378 scopus 로고    scopus 로고
    • Integrals over classical groups, random permutations, Toda and Toeplitz lattices
    • (math. C0/9912143)
    • M. ADLER and P. VAN MOERBEKE: Integrals over classical groups, random permutations, Toda and Toeplitz lattices, Comm. Pure Appl. Math. (2000) (math. C0/9912143).
    • (2000) Comm. Pure Appl. Math.
    • Adler, M.1    Van Moerbeke, P.2
  • 4
    • 0001769490 scopus 로고
    • Random matrices, vertex operators and the Virasoro algebra
    • M. ADLER, T. SHIOTA and P. VAN MOERBEKE: Random matrices, vertex operators and the Virasoro algebra, Phys. Lett. A 208, 101-112, (1995). And
    • (1995) Phys. Lett. A , vol.208 , pp. 101-112
    • Adler, M.1    Shiota, T.2    Van Moerbeke, P.3
  • 5
    • 0000177518 scopus 로고    scopus 로고
    • Random matrices, Virasoro algebras and non-commutative KP
    • Random matrices, Virasoro algebras and non-commutative KP, Duke Math. J. 94, 379-431 (1998).
    • (1998) Duke Math. J. , vol.94 , pp. 379-431
  • 6
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem
    • D. ALDOUS and P. DIACONIS: Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem, Bull. Am. Math. Soc. (new series) 36 (4), 413-432 (1999).
    • (1999) Bull. Am. Math. Soc. (New Series) , vol.36 , Issue.4 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 7
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • (math.C0/9810105)
    • [G] J. BAIK, P. DEIFT and K. JOHANSSON: On the distribution of the length of the longest increasing subsequence of random permutations, Math. Archive, Journal Amer. Math. Soc. 12, 1119-1178 (1999) (math.C0/9810105).
    • (1999) Math. Archive, Journal Amer. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 9
    • 33646859849 scopus 로고
    • Quantum field theory techniques in graphical enumeration
    • D. BESSIS, Cl. ITZYKSON and J.-B. ZUBER : Quantum field theory techniques in graphical enumeration, Adv. Appl. Math. 1, 109-157 (1980).
    • (1980) Adv. Appl. Math. , vol.1 , pp. 109-157
    • Bessis, D.1    Itzykson, C.2    Zuber, J.-B.3
  • 11
    • 0002704693 scopus 로고
    • Universal scaling of the tail of the density of eigenvalues in random matrix models
    • M. BOWICK and E. BRÉZIN: Universal scaling of the tail of the density of eigenvalues in random matrix models, Phys. Letters B 268, 21-28 (1991).
    • (1991) Phys. Letters B , vol.268 , pp. 21-28
    • Bowick, M.1    Brézin, E.2
  • 12
    • 0002123911 scopus 로고
    • A method of integration over matrix variables : II
    • S. CHADHA, G. MAHOUX, M.L. MEHTA : A method of integration over matrix variables : II, J. Phys. A: Math. Gen. 14, 579-586 (1981).
    • (1981) J. Phys. A: Math. Gen. , vol.14 , pp. 579-586
    • Chadha, S.1    Mahoux, G.2    Mehta, M.L.3
  • 13
    • 0039016041 scopus 로고    scopus 로고
    • Chazy classes IX-XII of third-order differential equations
    • C.M. COSGROVE: Chazy classes IX-XII of third-order differential equations, Stud. Appl. Math. 104, 3, 171-228 (2000).
    • (2000) Stud. Appl. Math. , vol.104 , Issue.3 , pp. 171-228
    • Cosgrove, C.M.1
  • 15
    • 0001086798 scopus 로고
    • A combinatorial theorem in geometry
    • P. ERDÖS and G. SZEKERES: A combinatorial theorem in geometry, Compositio Math., 2, 463-470 (1935).
    • (1935) Compositio Math. , vol.2 , pp. 463-470
    • Erdös, P.1    Szekeres, G.2
  • 16
    • 0001283085 scopus 로고
    • The isomonodromy approach to matrix models in 2d quantum gravity
    • A.S. FOKAS, A.R. ITS, A.V. KITAEV: The isomonodromy approach to matrix models in 2d quantum gravity, Comm. Math. Phys., 147, 395-430 (1992).
    • (1992) Comm. Math. Phys. , vol.147 , pp. 395-430
    • Fokas, A.S.1    Its, A.R.2    Kitaev, A.V.3
  • 17
    • 0000609652 scopus 로고
    • The spectrum edge of random matrix ensembles
    • P.J. FORRESTER: The spectrum edge of random matrix ensembles, Nucl. Phys. B, (1993).
    • (1993) Nucl. Phys. B
    • Forrester, P.J.1
  • 18
    • 0003166713 scopus 로고
    • Symmetric functions and P-recursiveness
    • I. M. GESSEL: Symmetric functions and P-recursiveness, J. of Comb. Theory, Ser A, 53, 257-285 (1990).
    • (1990) J. of Comb. Theory, Ser A , vol.53 , pp. 257-285
    • Gessel, I.M.1
  • 20
    • 0001292292 scopus 로고
    • Unitary matrix models and Painlevé III
    • M. HISAKADO: Unitary matrix models and Painlevé III, Mod. Phys. Letters, A 11 3001-3010 (1990).
    • (1990) Mod. Phys. Letters, A , vol.11 , pp. 3001-3010
    • Hisakado, M.1
  • 21
  • 22
    • 2342488264 scopus 로고
    • Density matrix of an impenetrable Base gas and the fifth Painlevé transcendent
    • M. JIMBO, T. MIWA, Y. MORI and M. SATO: Density matrix of an impenetrable Base gas and the fifth Painlevé transcendent, Physica ID, 80-158 (1980).
    • (1980) Physica ID , pp. 80-158
    • Jimbo, M.1    Miwa, T.2    Mori, Y.3    Sato, M.4
  • 23
    • 0032219317 scopus 로고    scopus 로고
    • The longest increasing subsequence in a random permutation and a unitary random matrix model
    • K. JOHANSSON: The Longest Increasing Subsequence in a Random Permutation and a Unitary Random Matrix Model, Math. Res. Lett., 5, no. 1-2, 63-82 (1998).
    • (1998) Math. Res. Lett. , vol.5 , Issue.1-2 , pp. 63-82
    • Johansson, K.1
  • 24
    • 0001345688 scopus 로고
    • A variational problem for random Young tableaux
    • B.F. LOGAN and L.A. SHEPP: A variational problem for random Young tableaux, Advances in Math., 26, 206-222 (1977).
    • (1977) Advances in Math. , vol.26 , pp. 206-222
    • Logan, B.F.1    Shepp, L.A.2
  • 25
    • 4244097913 scopus 로고
    • Universality of random-matrix predictions for the statistics of energy levels
    • R.D. KAMIEN, H.D. POLITZER, M.B. WISE: Universality of random-matrix predictions for the statistics of energy levels Phys. rev. letters 60, 1995-1998 (1988).
    • (1988) Phys. Rev. Letters , vol.60 , pp. 1995-1998
    • Kamien, R.D.1    Politzer, H.D.2    Wise, M.B.3
  • 26
    • 0001792752 scopus 로고
    • Intersection theory on the moduli space of curves and the matrix Airy function
    • M. KONTSEVICH: Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147, 1-23 (1992).
    • (1992) Comm. Math. Phys. , vol.147 , pp. 1-23
    • Kontsevich, M.1
  • 28
    • 0001564556 scopus 로고
    • A method of integration over matrix variables: IV
    • G. MAHOUX, M.L. MEHTA: A method of integration over matrix variables: IV, J. Phys. I (France) 1, 1093-1108 (1991).
    • (1991) J. Phys. I (France) , vol.1 , pp. 1093-1108
    • Mahoux, G.1    Mehta, M.L.2
  • 30
    • 0000817750 scopus 로고
    • Correlation functions of random matrix ensembles related to classical orthogonal polynomials
    • T. NAGAO, M. WADATI: Correlation functions of random matrix ensembles related to classical orthogonal polynomials, J. Phys. Soc of Japan, 60 3298-3322 (1991).
    • (1991) J. Phys. Soc of Japan , vol.60 , pp. 3298-3322
    • Nagao, T.1    Wadati, M.2
  • 33
    • 0000597238 scopus 로고
    • On the universality of the level spacing distribution for some ensembles of random matrices
    • L.A. PASTUR: On the universality of the level spacing distribution for some ensembles of random matrices, Letters Math. Phys., 25 259-265 (1992).
    • (1992) Letters Math. Phys. , vol.25 , pp. 259-265
    • Pastur, L.A.1
  • 35
    • 10044262136 scopus 로고    scopus 로고
    • Increasing subsequences and the classical groups
    • E. M. RAINS: Increasing subsequences and the classical groups, Elect. J. of Combinatorics, 5, R12 (1998).
    • (1998) Elect. J. of Combinatorics , vol.5
    • Rains, E.M.1
  • 36
    • 27644532196 scopus 로고
    • Level-spacings distribution and the Airy kernel
    • C.A. TRACY and H. WIDOM: Level-Spacings distribution and the Airy kernel, Commun. Math. Phys., 159, 151-174 (1994).
    • (1994) Commun. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.A.1    Widom, H.2
  • 39
    • 0002656386 scopus 로고
    • Monte Carlo calculations in problems of mathematical physics
    • E.F. Beckenbach ed., McGraw-Hill
    • S.M. ULAM: Monte Carlo calculations in problems of mathematical physics, in Modern Mathematics for the Engineers, E.F. Beckenbach ed., McGraw-Hill, 261-281 (1961).
    • (1961) Modern Mathematics for the Engineers , pp. 261-281
    • Ulam, S.M.1
  • 40
    • 0000789087 scopus 로고    scopus 로고
    • Integrable lattices: Random matrices and permutations
    • Eds.: P. Bleher, A. Its, Oxford University press, (math.C0/00-10)
    • P. VAN MOERBEKE: Integrable lattices: random matrices and permutations, MSRI-volume on Random matrices and exactly solvable models, Eds.: P. Bleher, A. Its, Oxford University press, 2000 (math.C0/00-10).
    • (2000) MSRI-volume on Random Matrices and Exactly Solvable Models
    • Van Moerbeke, P.1
  • 41
    • 0000057952 scopus 로고
    • Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux
    • A.M. VERSHIK and S.V. KEROV: Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux, Soviet Math. Dokl., 18, 527-531 (1977).
    • (1977) Soviet Math. Dokl. , vol.18 , pp. 527-531
    • Vershik, A.M.1    Kerov, S.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.