메뉴 건너뛰기




Volumn 127, Issue 6, 2007, Pages 1121-1165

From random matrices to stochastic operators

Author keywords

Random eigenvalues; Random matrices; Stochastic differential operators

Indexed keywords


EID: 34249901791     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9226-4     Document Type: Article
Times cited : (98)

References (24)
  • 1
    • 0036850051 scopus 로고    scopus 로고
    • Matrix models for beta ensembles
    • I. Dumitriu and A. Edelman, Matrix models for beta ensembles. J. Math. Phys. 43(11):5830-5847 (2002).
    • (2002) J. Math. Phys , vol.43 , Issue.11 , pp. 5830-5847
    • Dumitriu, I.1    Edelman, A.2
  • 2
    • 26844510449 scopus 로고    scopus 로고
    • Eigenvalues of Hermite and Laguerre ensembles: Large beta asymptotics
    • I. Dumitriu and A. Edelman, Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics. Ann. Inst. H. Poincaré Probab. Statist. 41(6):1083-1099 (2005).
    • (2005) Ann. Inst. H. Poincaré Probab. Statist , vol.41 , Issue.6 , pp. 1083-1099
    • Dumitriu, I.1    Edelman, A.2
  • 4
    • 44649173035 scopus 로고    scopus 로고
    • The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems
    • A. Edelman and B. D. Sutton, The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems. Found. Comput. Math.
    • Found. Comput. Math
    • Edelman, A.1    Sutton, B.D.2
  • 5
    • 0000609652 scopus 로고
    • The spectrum edge of random matrix ensembles
    • P. J. Forrester, The spectrum edge of random matrix ensembles. Nuclear Phys. B 402(3):709-728 (1993).
    • (1993) Nuclear Phys. B , vol.402 , Issue.3 , pp. 709-728
    • Forrester, P.J.1
  • 7
    • 2342488264 scopus 로고
    • Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
    • M. Jimbo, T. Miwa, Y. Môri, and M. Sato, Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1(1):80-158 (1980).
    • (1980) Phys. D , vol.1 , Issue.1 , pp. 80-158
    • Jimbo, M.1    Miwa, T.2    Môri, Y.3    Sato, M.4
  • 8
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • K. Johansson, Shape fluctuations and random matrices. Comm. Math. Phys. 209(2):437-476 (2000).
    • (2000) Comm. Math. Phys , vol.209 , Issue.2 , pp. 437-476
    • Johansson, K.1
  • 9
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29(2):295-327 (2001).
    • (2001) Ann. Statist , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 10
    • 8644242358 scopus 로고    scopus 로고
    • Matrix models for circular ensembles
    • R. Killip and I. Nenciu, Matrix models for circular ensembles. Int. Math. Res. Not. (50):2665-2701 (2004).
    • (2004) Int. Math. Res. Not , vol.50 , pp. 2665-2701
    • Killip, R.1    Nenciu, I.2
  • 11
    • 0036360694 scopus 로고    scopus 로고
    • Universality for eigenvalue correlations from the modified Jacobi unitary ensemble
    • 30):1575-1600 2002
    • A. B. J. Kuijlaars and M. Vanlessen, Universality for eigenvalue correlations from the modified Jacobi unitary ensemble. Int. Math. Res. Not. (30):1575-1600 (2002).
    • Int. Math. Res. Not
    • Kuijlaars, A.B.J.1    Vanlessen, M.2
  • 12
    • 0004163930 scopus 로고
    • 2nd ed, Academic Press Inc, Boston, MA
    • M. L. Mehta, Random Matrices, 2nd ed. (Academic Press Inc., Boston, MA, 1991).
    • (1991) Random Matrices
    • Mehta, M.L.1
  • 13
    • 34249871970 scopus 로고    scopus 로고
    • B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, 5th ed., (Springer-Verlag, Berlin, 2000).
    • B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, 5th ed., (Springer-Verlag, Berlin, 2000).
  • 14
    • 34249863921 scopus 로고    scopus 로고
    • Beta ensembles, stochastic airy spectrum, and a diffusion
    • Preprint
    • J. A. Ramírez, B. Rider, and Bálint Virág, Beta ensembles, stochastic airy spectrum, and a diffusion. Preprint.
    • Ramírez, J.A.1    Rider, B.2    Virág, B.3
  • 15
    • 0001629248 scopus 로고
    • The smallest eigenvalue of a large-dimensional Wishart matrix
    • J. W. Silverstein, The smallest eigenvalue of a large-dimensional Wishart matrix. Ann. Probab. 13(4):1364-1368 (1985).
    • (1985) Ann. Probab , vol.13 , Issue.4 , pp. 1364-1368
    • Silverstein, J.W.1
  • 17
    • 34249895348 scopus 로고    scopus 로고
    • G. Szego, Orthogonal Polynomials, XXIII, 4th ed. (American Mathematical Society, Providence, R.I., 1975. American Mathematical Society, Colloquium Publications).
    • G. Szego, Orthogonal Polynomials, vol. XXIII, 4th ed. (American Mathematical Society, Providence, R.I., 1975. American Mathematical Society, Colloquium Publications).
  • 18
    • 0000649044 scopus 로고
    • Introduction to random matrices
    • Geometric and Quantum Aspects of Integrable Systems Scheveningen, 1992, of, Springer, Berlin
    • C. A. Tracy and H. Widom, Introduction to random matrices. In Geometric and Quantum Aspects of Integrable Systems (Scheveningen, 1992), volume 424 of Lecture Notes in Phys., pp. 103-130. (Springer, Berlin 1993).
    • (1993) Lecture Notes in Phys , vol.424 , pp. 103-130
    • Tracy, C.A.1    Widom, H.2
  • 19
    • 13844256077 scopus 로고
    • Level-spacing distributions and the Airy kernel
    • C. A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel. Phys. Lett. B 305:115-118 (1993).
    • (1993) Phys. Lett. B , vol.305 , pp. 115-118
    • Tracy, C.A.1    Widom, H.2
  • 20
    • 27644532196 scopus 로고
    • Level-spacing distributions and the Airy kernel
    • C. A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159(1):151-174 (1994).
    • (1994) Comm. Math. Phys , vol.159 , Issue.1 , pp. 151-174
    • Tracy, C.A.1    Widom, H.2
  • 21
    • 0342395256 scopus 로고
    • Level spacing distributions and the Bessel kernel
    • C. A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel. Comm. Math. Phys. 161(2):289-309 (1994).
    • (1994) Comm. Math. Phys , vol.161 , Issue.2 , pp. 289-309
    • Tracy, C.A.1    Widom, H.2
  • 22
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • C. A. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177(3):727-754 (1996).
    • (1996) Comm. Math. Phys , vol.177 , Issue.3 , pp. 727-754
    • Tracy, C.A.1    Widom, H.2
  • 23
    • 34249867462 scopus 로고    scopus 로고
    • C. A. Tracy and H. Widom, The distribution of the largest eigenvalue in the Gaussian ensembles: β = 1, 2, 4. In Calogero-Moser-Sutherland Models (Montréal, QC, 1997), CRM Ser. Math. Phys., pp. 461-472. (Springer, New York, 2000).
    • C. A. Tracy and H. Widom, The distribution of the largest eigenvalue in the Gaussian ensembles: β = 1, 2, 4. In Calogero-Moser-Sutherland Models (Montréal, QC, 1997), CRM Ser. Math. Phys., pp. 461-472. (Springer, New York, 2000).
  • 24
    • 0011438216 scopus 로고
    • Eigenvalue distributions of large Hermitian matrices; Wigner's semicircle law and a theorem of Kac, Murdock, and Szegǒ
    • H. F. Trotter, Eigenvalue distributions of large Hermitian matrices; Wigner's semicircle law and a theorem of Kac, Murdock, and Szegǒ. Adv. Math. 54(1):67-82 (1984).
    • (1984) Adv. Math , vol.54 , Issue.1 , pp. 67-82
    • Trotter, H.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.