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Volumn 59, Issue 2, 2006, Pages 161-253

Averages of characteristic polynomials in random matrix theory

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EID: 33645353058     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20092     Document Type: Article
Times cited : (113)

References (60)
  • 1
    • 0034339813 scopus 로고    scopus 로고
    • Classical skew orthogonal polynomials and random matrices
    • Adler, M.; Forrester, P. J.; Nagao, T.; van Moerbeke, P. Classical skew orthogonal polynomials and random matrices. J. Statist. Phys. 99 (2000), no. 1-2, 141-170.
    • (2000) J. Statist. Phys. , vol.99 , Issue.1-2 , pp. 141-170
    • Adler, M.1    Forrester, P.J.2    Nagao, T.3    Van Moerbeke, P.4
  • 2
    • 0038441791 scopus 로고    scopus 로고
    • Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges
    • Akemann, G.; Fyodorov, Y. V. Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges. Nuclear Phys. B 664 (2003), no. 3, 457-476.
    • (2003) Nuclear Phys. B , vol.664 , Issue.3 , pp. 457-476
    • Akemann, G.1    Fyodorov, Y.V.2
  • 3
    • 0038814298 scopus 로고    scopus 로고
    • Characteristic polynomials of complex random matrix models
    • Akemann, G.; Vernizzi, G. Characteristic polynomials of complex random matrix models. Nuclear Phys. B 660 (2003), no. 3, 532-556.
    • (2003) Nuclear Phys. B , vol.660 , Issue.3 , pp. 532-556
    • Akemann, G.1    Vernizzi, G.2
  • 4
    • 0000335744 scopus 로고
    • Correlators of spectral determinants in quantum chaos
    • Andreev, A. V.; Simons, B. D. Correlators of spectral determinants in quantum chaos. Phys. Rev. Lett. 75 (1995), no. 12, 2304-2307.
    • (1995) Phys. Rev. Lett. , vol.75 , Issue.12 , pp. 2304-2307
    • Andreev, A.V.1    Simons, B.D.2
  • 5
    • 0043231262 scopus 로고    scopus 로고
    • Products and ratios of characteristic polynomials of random Hermitian matrices
    • Baik, J.; Deift, P.; Strahov, E. Products and ratios of characteristic polynomials of random Hermitian matrices. J. Math. Phys. 44 (2003), no. 8, 3657-3670.
    • (2003) J. Math. Phys. , vol.44 , Issue.8 , pp. 3657-3670
    • Baik, J.1    Deift, P.2    Strahov, E.3
  • 6
    • 0038578323 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: Announcement of results
    • Baik, J.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Miller, P. D. Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: announcement of results. Int. Math. Res. Not. 2003, no. 15, 821-858.
    • Int. Math. Res. Not. , vol.2003 , Issue.15 , pp. 821-858
    • Baik, J.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Miller, P.D.4
  • 7
    • 0010152218 scopus 로고    scopus 로고
    • Algebraic aspects of increasing subsequences
    • Baik, J.; Rains, E. Algebraic aspects of increasing subsequences. Duke Math. J. 109 (2001), no. 1, 1-65.
    • (2001) Duke Math. J. , vol.109 , Issue.1 , pp. 1-65
    • Baik, J.1    Rains, E.2
  • 8
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
    • Bleher, P.; Its, A. Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1999), no. 1, 185-266.
    • (1999) Ann. of Math. (2) , vol.150 , Issue.1 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 9
    • 0036390386 scopus 로고    scopus 로고
    • Duality of orthogonal polynomials on a finite set
    • Borodin, A. Duality of orthogonal polynomials on a finite set. J. Statist. Phys. 109 (2002), no. 5-6, 1109-1120.
    • (2002) J. Statist. Phys. , vol.109 , Issue.5-6 , pp. 1109-1120
    • Borodin, A.1
  • 10
    • 0034390399 scopus 로고    scopus 로고
    • Asymptotics of Plansherel measures for symmetric groups
    • Borodin, A.; Okounkov, A.; Olshanski, G. Asymptotics of Plansherel measures for symmetric groups. J. Amer. Math. Soc. 13 (2000), no. 3, 481-515.
    • (2000) J. Amer. Math. Soc. , vol.13 , Issue.3 , pp. 481-515
    • Borodin, A.1    Okounkov, A.2    Olshanski, G.3
  • 11
    • 0034349003 scopus 로고    scopus 로고
    • Distributions on partitions, point processes and the hypergeometric kernel
    • Borodin, A.; Olshanski, G. Distributions on partitions, point processes and the hypergeometric kernel. Comm. Math. Phys. 211 (2000), no. 2, 335-358.
    • (2000) Comm. Math. Phys. , vol.211 , Issue.2 , pp. 335-358
    • Borodin, A.1    Olshanski, G.2
  • 12
    • 85030924807 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
    • to appear
    • Borodin, A.; Olshanski, G. Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Ann. of Math. (2), to appear.
    • Ann. of Math. (2)
    • Borodin, A.1    Olshanski, G.2
  • 13
    • 16244409482 scopus 로고    scopus 로고
    • Random partitions and the Gamma kernel
    • to appear
    • Borodin, A.; Olshanski, G. Random partitions and the Gamma kernel. Adv. Math., to appear.
    • Adv. Math.
    • Borodin, A.1    Olshanski, G.2
  • 14
    • 3543028406 scopus 로고    scopus 로고
    • Z-measures on partitions and their scaling limits
    • to appear
    • Borodin, A.; Olshanski, G. Z-measures on partitions and their scaling limits. European J. Combin., to appear.
    • European J. Combin.
    • Borodin, A.1    Olshanski, G.2
  • 15
    • 0034348204 scopus 로고    scopus 로고
    • Characteristic polynomials of random matrices
    • Brézin, E.; Hikami, S. Characteristic polynomials of random matrices. Comm. Math. Phys. 214 (2000), no. 1, 111-135.
    • (2000) Comm. Math. Phys. , vol.214 , Issue.1 , pp. 111-135
    • Brézin, E.1    Hikami, S.2
  • 16
    • 0038815126 scopus 로고    scopus 로고
    • Characteristic polynomials of random matrices at edge singularities
    • Brézin, E.; Hikami, S. Characteristic polynomials of random matrices at edge singularities. Phys. Rev. E (3) 62 (2000), no. 3, part A, 3558-3567.
    • (2000) Phys. Rev. E (3) , vol.62 , Issue.3 PART A , pp. 3558-3567
    • Brézin, E.1    Hikami, S.2
  • 17
    • 0035540541 scopus 로고    scopus 로고
    • Characteristic polynomials of real symmetric random matrices
    • Brézin, E.; Hikami, S. Characteristic polynomials of real symmetric random matrices. Comm. Math. Phys. 223 (2001), no. 2, 363-382.
    • (2001) Comm. Math. Phys. , vol.223 , Issue.2 , pp. 363-382
    • Brézin, E.1    Hikami, S.2
  • 18
    • 0242266603 scopus 로고    scopus 로고
    • New correlation functions for random matrices and integrals over super-groups
    • Brézin, E.; Hikami, S. New correlation functions for random matrices and integrals over super-groups. J. Phys. A 36 (2003), no. 3, 711-751.
    • (2003) J. Phys. A , vol.36 , Issue.3 , pp. 711-751
    • Brézin, E.1    Hikami, S.2
  • 21
    • 0001395985 scopus 로고
    • On some multiple integrals involving determinants
    • de Bruijn, N. G. On some multiple integrals involving determinants. J. Indian. Math. Soc. (N.S.) 19 (1955), 133-151.
    • (1955) J. Indian. Math. Soc. (N.S.) , vol.19 , pp. 133-151
    • De Bruijn, N.G.1
  • 22
    • 0003608444 scopus 로고    scopus 로고
    • Courant Lecture Notes in Mathematics, 3. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, R.I.
    • Deift, P. Orthogonal polynomials and random matrices: a Riemann-Hilbert approach. Courant Lecture Notes in Mathematics, 3. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, R.I., 1999.
    • (1999) Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
    • Deift, P.1
  • 23
    • 33645338277 scopus 로고    scopus 로고
    • Deift, P.; Gioev, D. In preparation
    • Deift, P.; Gioev, D. In preparation.
  • 25
    • 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.; Zhou, X. A. 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), no. 11, 1335-1425.
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.11 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.A.5
  • 27
    • 0035929535 scopus 로고    scopus 로고
    • Asymptotics of skew orthogonal polynomials
    • Eynard, B. Asymptotics of skew orthogonal polynomials. J. Phys. A 34 (2001), no. 37, 7591-7605.
    • (2001) J. Phys. A , vol.34 , Issue.37 , pp. 7591-7605
    • Eynard, B.1
  • 29
    • 4744349420 scopus 로고    scopus 로고
    • Singularity dominated strong fluctuations for some random matrix averages
    • Forrester, P. J.; Keating, J. P. Singularity dominated strong fluctuations for some random matrix averages. Comm. Math. Phys. 250 (2004), no. 1, 119-131.
    • (2004) Comm. Math. Phys. , vol.250 , Issue.1 , pp. 119-131
    • Forrester, P.J.1    Keating, J.P.2
  • 30
    • 0033516823 scopus 로고    scopus 로고
    • Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
    • Forrester, P. J.; Nagao, T.; Honner, G. Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges. Nucl. Phys. B 553 (1999), no. 3, 601-643.
    • (1999) Nucl. Phys. B , vol.553 , Issue.3 , pp. 601-643
    • Forrester, P.J.1    Nagao, T.2    Honner, G.3
  • 31
    • 0037147842 scopus 로고    scopus 로고
    • Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
    • Fyodorov, Y. V. Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation. Nuclear Phys. B 621 (2002), no. 3, 643-674.
    • (2002) Nuclear Phys. B , vol.621 , Issue.3 , pp. 643-674
    • Fyodorov, Y.V.1
  • 32
    • 8644235035 scopus 로고    scopus 로고
    • Erratum: Complexity of random energy landscapes, glass transition and absolute value of spectral determinant of random matrices
    • Fyodorov, Y. V. Erratum: Complexity of random energy landscapes, glass transition and absolute value of spectral determinant of random matrices. Phys. Rev. Lett. 93 (2004), 149901(E).
    • (2004) Phys. Rev. Lett. , vol.93
    • Fyodorov, Y.V.1
  • 33
    • 1242289597 scopus 로고    scopus 로고
    • On the supersymmetric partition function in QCD-inspired random matrix models
    • Fyodorov, Y. V.; Akemann, G. On the supersymmetric partition function in QCD-inspired random matrix models. JETP Lett. 77 (2003), no. 8, 438-441.
    • (2003) JETP Lett. , vol.77 , Issue.8 , pp. 438-441
    • Fyodorov, Y.V.1    Akemann, G.2
  • 34
    • 0037432888 scopus 로고    scopus 로고
    • Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations
    • Fyodorov, Y. V.; Keating, J. P. Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations. J. Phys. A 36 (2003), no. 14, 4035-4046.
    • (2003) J. Phys. A , vol.36 , Issue.14 , pp. 4035-4046
    • Fyodorov, Y.V.1    Keating, J.P.2
  • 36
    • 0037141116 scopus 로고    scopus 로고
    • Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kähler manifolds
    • Fyodorov, Y. V.; Strahov, E. Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kähler manifolds. Nucl. Phys. B 630 (2002), no. 3, 453-491.
    • (2002) Nucl. Phys. B , vol.630 , Issue.3 , pp. 453-491
    • Fyodorov, Y.V.1    Strahov, E.2
  • 37
    • 0037203026 scopus 로고    scopus 로고
    • On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble
    • Fyodorov, Y. V.; Strahov, E. On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble. Nuclear Phys. B 647 (2002), no. 3, 581-597.
    • (2002) Nuclear Phys. B , vol.647 , Issue.3 , pp. 581-597
    • Fyodorov, Y.V.1    Strahov, E.2
  • 38
    • 0037471259 scopus 로고    scopus 로고
    • An exact formula for general spectral correlation function of random Hermitian matrices
    • Fyodorov, Y. V.; Strahov, E. An exact formula for general spectral correlation function of random Hermitian matrices. J. Phys. A 36 (2003), no. 12, 3203-3213.
    • (2003) J. Phys. A , vol.36 , Issue.12 , pp. 3203-3213
    • Fyodorov, Y.V.1    Strahov, E.2
  • 39
    • 1342326180 scopus 로고    scopus 로고
    • The k-point random matrix kernels obtained from one-point supermatrix models
    • Gronqvist, J.; Guhr, T.; Kohler, H. The k-point random matrix kernels obtained from one-point supermatrix models. J. Phys. A 37 (2004), no. 6, 2331-2344.
    • (2004) J. Phys. A , vol.37 , Issue.6 , pp. 2331-2344
    • Gronqvist, J.1    Guhr, T.2    Kohler, H.3
  • 40
    • 0035535736 scopus 로고    scopus 로고
    • On the characteristic polynomial of a random unitary matrix
    • Hughes, C. P.; Keating, J. P.; O'Connell, N. On the characteristic polynomial of a random unitary matrix. Comm. Math. Phys. 220 (2001), no. 2, 429-451.
    • (2001) Comm. Math. Phys. , vol.220 , Issue.2 , pp. 429-451
    • Hughes, C.P.1    Keating, J.P.2    O'Connell, N.3
  • 41
    • 0036628218 scopus 로고    scopus 로고
    • Non-intersecting paths, random tilings and random matrices
    • Johansson, K. Non-intersecting paths, random tilings and random matrices. Probab. Theory Related Fields 123 (2002), no. 2, 225-280.
    • (2002) Probab. Theory Related Fields , vol.123 , Issue.2 , pp. 225-280
    • Johansson, K.1
  • 42
    • 0034348205 scopus 로고    scopus 로고
    • Random matrix theory and L-functions at s = 1/2
    • Keating, J. P.; Snaith, N. C. Random matrix theory and L-functions at s = 1/2. Comm. Math. Phys. 214 (2000), no. 1, 91-110.
    • (2000) Comm. Math. Phys. , vol.214 , Issue.1 , pp. 91-110
    • Keating, J.P.1    Snaith, N.C.2
  • 43
    • 0034288949 scopus 로고    scopus 로고
    • Random matrix theory and ζ(1/2 + it)
    • Keating, J. P.; Snaith, N. C. Random matrix theory and ζ(1/2 + it). Comm. Math. Phys. 214 (2000), no. 1, 57-89.
    • (2000) Comm. Math. Phys. , vol.214 , Issue.1 , pp. 57-89
    • Keating, J.P.1    Snaith, N.C.2
  • 44
    • 1842709153 scopus 로고    scopus 로고
    • The boundary of the Young graph with Jack edge multiplicities
    • Kerov, S.; Okounkov, A.; Olshanski, G. The boundary of the Young graph with Jack edge multiplicities. Int. Math. Res. Notes. 4 (1998), 173-199.
    • (1998) Int. Math. Res. Notes. , vol.4 , pp. 173-199
    • Kerov, S.1    Okounkov, A.2    Olshanski, G.3
  • 46
    • 0039251933 scopus 로고    scopus 로고
    • Moments of the characteristic polynomial in the three ensembles of random matrices
    • Mehta, M.; Normand, J. M. Moments of the characteristic polynomial in the three ensembles of random matrices. J. Phys. A 34 (2001), no. 22, 4627-4639.
    • (2001) J. Phys. A , vol.34 , Issue.22 , pp. 4627-4639
    • Mehta, M.1    Normand, J.M.2
  • 47
    • 0000540882 scopus 로고    scopus 로고
    • Vicious random walkers and a discretization of Gaussian random matrix ensembles
    • Nagao, T.; Forrester, P. J. Vicious random walkers and a discretization of Gaussian random matrix ensembles. Nuclear Phys. B 620 (2002), no. 3, 551-565.
    • (2002) Nuclear Phys. B , vol.620 , Issue.3 , pp. 551-565
    • Nagao, T.1    Forrester, P.J.2
  • 48
    • 0010028379 scopus 로고
    • Correlation functions of random matrix ensembles related to classical orthogonal polynomials. III
    • Nagao, T.; Wadati, M. Correlation functions of random matrix ensembles related to classical orthogonal polynomials. III. J. Phys. Soc. Japan 61 (1992), no. 6, 1910-1918.
    • (1992) J. Phys. Soc. Japan , vol.61 , Issue.6 , pp. 1910-1918
    • Nagao, T.1    Wadati, M.2
  • 51
    • 0034556390 scopus 로고    scopus 로고
    • Determinantal random point fields
    • Soshnikov, A. Determinantal random point fields. Russian Math. Surveys 55 (2000), no. 5, 923-975.
    • (2000) Russian Math. Surveys , vol.55 , Issue.5 , pp. 923-975
    • Soshnikov, A.1
  • 52
    • 0346672420 scopus 로고    scopus 로고
    • Janossy densities. II. Pfaffian ensembles
    • Soshnikov, A. Janossy densities. II. Pfaffian ensembles. J. Statist. Phys. 113 (2003), no. 3-4, 611-622.
    • (2003) J. Statist. Phys. , vol.113 , Issue.3-4 , pp. 611-622
    • Soshnikov, A.1
  • 53
    • 0242370751 scopus 로고    scopus 로고
    • Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach
    • Strahov, E.; Fyodorov, Y. V. Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach. Comm. Math. Phys. 241 (2003), no. 2-3, 343-382.
    • (2003) Comm. Math. Phys. , vol.241 , Issue.2-3 , pp. 343-382
    • Strahov, E.1    Fyodorov, Y.V.2
  • 54
    • 0035911858 scopus 로고    scopus 로고
    • Microscopic spectrum of the QCD Dirac operator in three dimensions
    • Szabo, R. J. Microscopic spectrum of the QCD Dirac operator in three dimensions. Nuclear Phys. B 598 (2001), no. 1-2, 309-347.
    • (2001) Nuclear Phys. B , vol.598 , Issue.1-2 , pp. 309-347
    • Szabo, R.J.1
  • 55
    • 84858583097 scopus 로고
    • American Mathematical Society Colloquium Publications, 23. American Mathematical Society, Providence, R.I.
    • Szegö, G. Orthogonal polynomials. 4th ed. American Mathematical Society Colloquium Publications, 23. American Mathematical Society, Providence, R.I., 1975.
    • (1975) Orthogonal Polynomials. 4th Ed.
    • Szegö, G.1
  • 56
    • 0032163852 scopus 로고    scopus 로고
    • Correlation functions, cluster functions, and spacing distributions of random matrices
    • Tracy, C. A.; Widom, H. Correlation functions, cluster functions, and spacing distributions of random matrices. J. Statist. Phys. 92 (1998), no. 5-6, 809-835.
    • (1998) J. Statist. Phys. , vol.92 , Issue.5-6 , pp. 809-835
    • Tracy, C.A.1    Widom, H.2
  • 57
    • 12444273769 scopus 로고    scopus 로고
    • Universal behavior for averages of characteristic polynomials at the origin of the spectrum
    • Vanlessen, M. Universal behavior for averages of characteristic polynomials at the origin of the spectrum. Comm. Math. Phys. 253 (2005), no. 3, 535-560.
    • (2005) Comm. Math. Phys. , vol.253 , Issue.3 , pp. 535-560
    • Vanlessen, M.1
  • 59
    • 0033074163 scopus 로고    scopus 로고
    • On the relation between orthogonal, symplectic and unitary random matrices
    • Widom, H. On the relation between orthogonal, symplectic and unitary random matrices. J. Statist. Phys. 94 (1999), no. 3-4, 347-364.
    • (1999) J. Statist. Phys. , vol.94 , Issue.3-4 , pp. 347-364
    • Widom, H.1
  • 60
    • 0030515852 scopus 로고    scopus 로고
    • Riemannian symmetric superspaces and their origin in random-matrix theory
    • Zirnbauer, M. R. Riemannian symmetric superspaces and their origin in random-matrix theory. J. Math. Phys. 37 (1996), no. 10, 4986-5018.
    • (1996) J. Math. Phys. , vol.37 , Issue.10 , pp. 4986-5018
    • Zirnbauer, M.R.1


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