메뉴 건너뛰기




Volumn 9, Issue 1, 2006, Pages 23-52

The PDEs of biorthogonal polynomials arising in the two-matrix model

Author keywords

Biorthogonal polynomials; Two matrix models

Indexed keywords


EID: 33745603443     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11040-005-9000-x     Document Type: Article
Times cited : (11)

References (22)
  • 1
    • 0005921172 scopus 로고    scopus 로고
    • String-orthogonal polynomials, string equations and 2-Toda symmetries
    • Adler M. and Van Moerbeke, P.; String-orthogonal polynomials, string equations and 2-Toda symmetries, Comm. Pure Appl. Math. J. 50 (1997), 241-290.
    • (1997) Comm. Pure Appl. Math. J. , vol.50 , pp. 241-290
    • Adler, M.1    Van Moerbeke, P.2
  • 2
    • 0033439997 scopus 로고    scopus 로고
    • The spectrum of coupled random matrices
    • Adler, M. and Van Moerbeke, P.: The spectrum of coupled random matrices, Ann. of Math. (2) 149 (1999), 921-976.
    • (1999) Ann. of Math. (2) , vol.149 , pp. 921-976
    • Adler, M.1    Van Moerbeke, P.2
  • 3
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
    • Bleher, P. and Its, A.: Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model, Ann. of Math. (2) 150(1) (1999), 185-266.
    • (1999) Ann. of Math. (2) , vol.150 , Issue.1 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 4
    • 0033440723 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
    • Deift, P., Kriecherbauer, T., McLaughlin, K. T. R., Venakides, S. and Zhou, Z.: Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52 (1999), 1335-1425.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.R.3    Venakides, S.4    Zhou, Z.5
  • 6
    • 0001283085 scopus 로고
    • The isomonodromy approach to matrix models in 2D quantum gravity
    • Fokas, A., Its, A. and Kitaev, A.: The isomonodromy approach to matrix models in 2D quantum gravity, Comm. Math. Phys. 147 (1992), 395-430.
    • (1992) Comm. Math. Phys. , vol.147 , pp. 395-430
    • Fokas, A.1    Its, A.2    Kitaev, A.3
  • 7
    • 0037471328 scopus 로고    scopus 로고
    • Partition functions for matrix models and isomonodromic tau functions
    • Bertola, M., Eynard, B. and Harnad, J.: Partition functions for matrix models and isomonodromic tau functions, J. Phys. A 36 (2003), 3067-3083.
    • (2003) J. Phys. A , vol.36 , pp. 3067-3083
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 8
    • 0346995411 scopus 로고    scopus 로고
    • Differential systems for bi-orthogonal polynomials appearing in two-matrix models and the associated Riemann-Hilbert problem
    • Bertola, M., Eynard, B. and Harnad, J.: Differential systems for bi-orthogonal polynomials appearing in two-matrix models and the associated Riemann-Hilbert problem, Comm. Math. Phys. 243 (2003), 193-240.
    • (2003) Comm. Math. Phys. , vol.243 , pp. 193-240
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 9
    • 0038407689 scopus 로고    scopus 로고
    • The Riemann-Hilbert problem for the bi-orthogonal polynomials
    • Kapaev, A. A.: The Riemann-Hilbert problem for the bi-orthogonal polynomials, J. Phys. A 36 (2003), 4629-4640.
    • (2003) J. Phys. A , vol.36 , pp. 4629-4640
    • Kapaev, A.A.1
  • 10
    • 0036024881 scopus 로고    scopus 로고
    • Duality, biorthogonal polynomials and multi-matrix models
    • Bertola, M., Eynard, B. and Harnad, J.: Duality, biorthogonal polynomials and multi-matrix models, Comm. Math. Phys. 229 (2002), 73-120.
    • (2002) Comm. Math. Phys. , vol.229 , pp. 73-120
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 11
    • 0037232418 scopus 로고    scopus 로고
    • Duality of spectral curves arising in two-matrix models
    • Bertola, M., Eynard, B. and Harnad, J.: Duality of spectral curves arising in two-matrix models, Theor. and Math. Phys. 134(1) (2003), 27-32.
    • (2003) Theor. and Math. Phys. , vol.134 , Issue.1 , pp. 27-32
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 12
    • 17144426793 scopus 로고
    • Ising model on a dynamical planar random lattice: Exact solution
    • Kazakov, V. A.: Ising model on a dynamical planar random lattice: exact solution, Phys. Lett. A 119 (1986), 140-144.
    • (1986) Phys. Lett. A , vol.119 , pp. 140-144
    • Kazakov, V.A.1
  • 13
    • 0000200923 scopus 로고
    • Rational theories of 2D gravity from the two-matrix model
    • hep-th/9303093
    • Daul, J. M., Kazakov, V. and Kostov, I. K.: Rational theories of 2D gravity from the two-matrix model, Nuclear Phys. B 409 (1993), 311-338, hep-th/9303093.
    • (1993) Nuclear Phys. B , vol.409 , pp. 311-338
    • Daul, J.M.1    Kazakov, V.2    Kostov, I.K.3
  • 15
    • 38249018616 scopus 로고
    • Estimates of asymmetric Freud polynomials on the real line
    • Bauldry, W.: Estimates of asymmetric Freud polynomials on the real line, J. Approx. Theory 63 (1990), 225-237.
    • (1990) J. Approx. Theory , vol.63 , pp. 225-237
    • Bauldry, W.1
  • 16
    • 38249017227 scopus 로고
    • Estimates of the Hermite and the Freud polynomials
    • Bonan, S. S. and Clark, D. S.: Estimates of the Hermite and the Freud polynomials, J. Approx. Theory 63 (1990), 210-224.
    • (1990) J. Approx. Theory , vol.63 , pp. 210-224
    • Bonan, S.S.1    Clark, D.S.2
  • 17
    • 49149137872 scopus 로고
    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients I
    • Jimbo, M., Miwa, T. and Ueno, K.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients I, Physica D 2 (1981), 306-352.
    • (1981) Physica D , vol.2 , pp. 306-352
    • Jimbo, M.1    Miwa, T.2    Ueno, K.3
  • 18
    • 49049148970 scopus 로고
    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II, III
    • Jimbo, M. and Miwa, T.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II, III, Physica D 2 (1981), 407-448;
    • (1981) Physica D , vol.2 , pp. 407-448
    • Jimbo, M.1    Miwa, T.2
  • 19
    • 49049152822 scopus 로고
    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II, III
    • Jimbo, M. and Miwa, T.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II, III, Physica ibid., D 4, 26-46 (1981).
    • (1981) Physica D , vol.4 , pp. 26-46
    • Jimbo, M.1    Miwa, T.2
  • 20
    • 0037356057 scopus 로고    scopus 로고
    • Bilinear semi-classical moment functionals and their integral representation
    • Bertola, M.: Bilinear semi-classical moment functionals and their integral representation, J. Approx. Theory 121 (2003), 71-99.
    • (2003) J. Approx. Theory , vol.121 , pp. 71-99
    • Bertola, M.1
  • 21
    • 0032523672 scopus 로고    scopus 로고
    • Matrices coupled in a chain: Eigenvalue correlations
    • condmat/9710230
    • Eynard, B. and Mehta, M. L.: Matrices coupled in a chain: eigenvalue correlations, J. Phys. A, Math. Gen. 31 (1998), 4449, condmat/9710230.
    • (1998) J. Phys. A, Math. Gen. , vol.31 , pp. 4449
    • Eynard, B.1    Mehta, M.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.