메뉴 건너뛰기




Volumn 60, Issue 9, 2007, Pages 1261-1292

PDEs for the Gaussian ensemble with external source and the pearcey distribution

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34547829712     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20175     Document Type: Article
Times cited : (47)

References (27)
  • 1
    • 0001769490 scopus 로고
    • Random matrices, vertex operators and the Virasoro algebra
    • Adler, M.; Shiota, T.; van Moerbeke, P. Random matrices, vertex operators and the Virasoro algebra. Phys. Lett. A 208 (1995), no. 1-2, 67-78.
    • (1995) Phys. Lett. A , vol.208 , Issue.1-2 , pp. 67-78
    • Adler, M.1    Shiota, T.2    van Moerbeke, P.3
  • 2
    • 0033439997 scopus 로고    scopus 로고
    • The spectrum of coupled random matrices
    • Adler, M.; van Moerbeke, P. The spectrum of coupled random matrices. Ann. of Math. (2) 149 (1999), no. 3, 921-976.
    • (1999) Ann. of Math. (2) , vol.149 , Issue.3 , pp. 921-976
    • Adler, M.1    van Moerbeke, P.2
  • 3
    • 0035595523 scopus 로고    scopus 로고
    • Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum
    • Adler, M.; van Moerbeke, P. Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum. Ann. of Math. (2) 153 (2001), no. 1, 149-189.
    • (2001) Ann. of Math. (2) , vol.153 , Issue.1 , pp. 149-189
    • Adler, M.1    van Moerbeke, P.2
  • 4
    • 23244433542 scopus 로고    scopus 로고
    • PDEs for the joint distributions of the Dyson, Airy and sine processes
    • Adler, M.; van Moerbeke, P. PDEs for the joint distributions of the Dyson, Airy and sine processes. Ann. Probab. 33 (2005), no. 4, 1326-1361.
    • (2005) Ann. Probab , vol.33 , Issue.4 , pp. 1326-1361
    • Adler, M.1    van Moerbeke, P.2
  • 5
    • 34547851226 scopus 로고    scopus 로고
    • Moment matrices and multi-component KP, with applications to random matrix theory
    • arXiv: math-ph/0612064
    • Adler, M.; van Moerbeke, P.; Vanhaecke, P. Moment matrices and multi-component KP, with applications to random matrix theory. arXiv: math-ph/0612064, 2006.
    • (2006)
    • Adler, M.1    van Moerbeke, P.2    Vanhaecke, P.3
  • 6
    • 24144459114 scopus 로고    scopus 로고
    • Large n limit of Gaussian random matrices with external source. II
    • arXiv: mathph/0408041
    • Aptekarev, A. I.; Bleher, P. M.; Kuijlaars, A. B. J. Large n limit of Gaussian random matrices with external source. II. Comm. Math. Phys. 259 (2005), no. 2, 367-389. arXiv: mathph/0408041, 2004.
    • (2004) Comm. Math. Phys , vol.259 , Issue.2 , pp. 367-389
    • Aptekarev, A.I.1    Bleher, P.M.2    Kuijlaars, A.B.J.3
  • 7
    • 0242382112 scopus 로고    scopus 로고
    • Aptekarev, A. I.;Braque; Branquinho, A.; Van Assche, W. Multiple orthogonal polynomials for classical weights. Trans. Amer. Math. Soc. 355 (2003), no. 10, 3887-3914 (electronic).
    • Aptekarev, A. I.;Braque; Branquinho, A.; Van Assche, W. Multiple orthogonal polynomials for classical weights. Trans. Amer. Math. Soc. 355 (2003), no. 10, 3887-3914 (electronic).
  • 8
    • 11244356563 scopus 로고    scopus 로고
    • Bleher, P.; Kuijlaars, A. B. J. Large n limit of Gaussian random matrices with external source. I. Comm. Math. Phys. 252 (2004), no. 1-3, 43-76. arXive: math-ph/040204, 2004.
    • Bleher, P.; Kuijlaars, A. B. J. Large n limit of Gaussian random matrices with external source. I. Comm. Math. Phys. 252 (2004), no. 1-3, 43-76. arXive: math-ph/040204, 2004.
  • 9
    • 1342290290 scopus 로고    scopus 로고
    • Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not. 2004, no. 3, 109-129
    • arXiv: math-ph/0307055
    • Bleher, P. M.; Kuijlaars, A. B. J. Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not. 2004, no. 3, 109-129. arXiv: math-ph/0307055, 2003.
    • (2003)
    • Bleher, P.M.1    Kuijlaars, A.B.J.2
  • 10
    • 0030592669 scopus 로고    scopus 로고
    • Correlations of nearby levels induced by a random potential
    • Brézin, E.; Hikami, S. Correlations of nearby levels induced by a random potential. Nuclear Phys. B 479 (1996), no. 3, 697-706.
    • (1996) Nuclear Phys. B , vol.479 , Issue.3 , pp. 697-706
    • Brézin, E.1    Hikami, S.2
  • 11
    • 4243508492 scopus 로고    scopus 로고
    • Extension of level spacing universality
    • Brézin, E.; Hikami, S. Extension of level spacing universality. Phys. Rev. E 56 (1997), no. 1, 264-269.
    • (1997) Phys. Rev. E , vol.56 , Issue.1 , pp. 264-269
    • Brézin, E.1    Hikami, S.2
  • 12
    • 0010481023 scopus 로고    scopus 로고
    • Brézin, E.; Hikami, S. Level spacing of random matrices in an external source. Phys. Rev. E (3) 58 (1998), no. 6, part A, 7176-7185.
    • Brézin, E.; Hikami, S. Level spacing of random matrices in an external source. Phys. Rev. E (3) 58 (1998), no. 6, part A, 7176-7185.
  • 13
    • 0032050389 scopus 로고    scopus 로고
    • Universal singularity at the closure of a gap in a random matrix theory
    • Brézin, E.; Hikami, S. Universal singularity at the closure of a gap in a random matrix theory. Phys. Rev. E (3) 57 (1998), no. 4, 4140-4149.
    • (1998) Phys. Rev. E (3) , vol.57 , Issue.4 , pp. 4140-4149
    • Brézin, E.1    Hikami, S.2
  • 15
    • 0041637573 scopus 로고
    • Brownian-motion model for the eigenvalues of a random matrix
    • Dyson, F. J. A Brownian-motion model for the eigenvalues of a random matrix. J. Mathematical Phys. 3 (1962), 1191-1198.
    • (1962) J. Mathematical Phys , vol.3 , pp. 1191-1198
    • Dyson, F.J.A.1
  • 16
    • 0033089822 scopus 로고    scopus 로고
    • Brownian motion in a Weyl chamber, non-colliding particles, and random matrices
    • Grabiner, D. J. Brownian motion in a Weyl chamber, non-colliding particles, and random matrices. Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), no. 2, 177-204.
    • (1999) Ann. Inst. H. Poincaré Probab. Statist , vol.35 , Issue.2 , pp. 177-204
    • Grabiner, D.J.1
  • 17
    • 0000458460 scopus 로고
    • Unitary and Hermitian matrices in an external field
    • Gross, D. J.; Newman, M. J. Unitary and Hermitian matrices in an external field. Phys. Lett. B 266 (1991), no. 3-4, 291-297.
    • (1991) Phys. Lett. B , vol.266 , Issue.3-4 , pp. 291-297
    • Gross, D.J.1    Newman, M.J.2
  • 18
    • 0035530553 scopus 로고    scopus 로고
    • Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices
    • Johansson, K. Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices. Comm. Math. Phys. 215 (2001), no. 3, 683-705.
    • (2001) Comm. Math. Phys , vol.215 , Issue.3 , pp. 683-705
    • Johansson, K.1
  • 19
    • 84972545947 scopus 로고
    • Coincidence probabilities
    • Karlin, S.; McGregor, J. Coincidence probabilities. Pacific J. Math. 9 (1959), 1141-1164,
    • (1959) Pacific J. Math , vol.9 , pp. 1141-1164
    • Karlin, S.1    McGregor, J.2
  • 20
    • 0011685696 scopus 로고
    • Exactly solvable Potts models, bond- and tree-like percolation on dynamical (random) planar lattice. Field theory on the lattice (Seillac, 1987)
    • Kazakov, V. A. Exactly solvable Potts models, bond- and tree-like percolation on dynamical (random) planar lattice. Field theory on the lattice (Seillac, 1987). Nuclear Phys. B Proc. Suppl. 4 (1988), 93-97.
    • (1988) Nuclear Phys. B Proc. Suppl , vol.4 , pp. 93-97
    • Kazakov, V.A.1
  • 21
    • 33846544971 scopus 로고    scopus 로고
    • Random skew plane partitions and the Pearcey process
    • arXiv: math.CO/0503508
    • Okounkov, A.; Reshetikhin, N. Random skew plane partitions and the Pearcey process. arXiv: math.CO/0503508, 2005.
    • (2005)
    • Okounkov, A.1    Reshetikhin, N.2
  • 22
    • 0002728031 scopus 로고
    • The spectrum of random matrices
    • Pastur, L. A. The spectrum of random matrices. Teoret. Mat. Fiz. 10 (1972), no. 1, 102-112.
    • (1972) Teoret. Mat. Fiz , vol.10 , Issue.1 , pp. 102-112
    • Pastur, L.A.1
  • 23
    • 0000379784 scopus 로고
    • The structure of an electromagnetic field in the neighborhood of a cusp of a caustic
    • Pearcey, T. The structure of an electromagnetic field in the neighborhood of a cusp of a caustic. Philos. Mag. 37 (1946), 311-317.
    • (1946) Philos. Mag , vol.37 , pp. 311-317
    • Pearcey, T.1
  • 24
    • 33644587270 scopus 로고    scopus 로고
    • The Pearcey process. Comm. Math. Phys. 263 (2006), no. 2, 381-400
    • arXiv: math.PR/0412005
    • Tracy, C. A.; Widom, H. The Pearcey process. Comm. Math. Phys. 263 (2006), no. 2, 381-400. arXiv: math.PR/0412005, 2005.
    • (2005)
    • Tracy, C.A.1    Widom, H.2
  • 26
    • 0031589479 scopus 로고    scopus 로고
    • Random Hermitian matrices in an external field
    • Zinn-Justin, P. Random Hermitian matrices in an external field. Nuclear Phys. B 497 (1997), no. 3, 725-732.
    • (1997) Nuclear Phys. B , vol.497 , Issue.3 , pp. 725-732
    • Zinn-Justin, P.1
  • 27
    • 0032474388 scopus 로고    scopus 로고
    • Universality of correlation functions of Hermitian random matrices in an external field
    • Zinn-Justin, P, Universality of correlation functions of Hermitian random matrices in an external field. Comm. Math. Phys. 194 (1998), no. 3, 631-650.
    • (1998) Comm. Math. Phys , vol.194 , Issue.3 , pp. 631-650
    • Zinn-Justin, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.