메뉴 건너뛰기




Volumn 200, Issue 3, 1999, Pages 661-683

Distribution of zeros of random and quantum chaotic sections of positive line bundles

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033514098     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050544     Document Type: Article
Times cited : (218)

References (33)
  • 1
    • 0031184913 scopus 로고    scopus 로고
    • Correlations between zeros of a random polynomial
    • [BD] Bleher, P. and Di, X.: Correlations between zeros of a random polynomial. J. Stat. Phys. 88, 269-305 (1997)
    • (1997) J. Stat. Phys. , vol.88 , pp. 269-305
    • Bleher, P.1    Di, X.2
  • 2
    • 84960576553 scopus 로고
    • On the roots of certain algebraic equations
    • [BP] Bloch, A. and Polya, G.: On the roots of certain algebraic equations. Proc. London Math. Soc. 33, 102-114 (1932)
    • (1932) Proc. London Math. Soc. , vol.33 , pp. 102-114
    • Bloch, A.1    Polya, G.2
  • 3
    • 0040517372 scopus 로고    scopus 로고
    • Quantum chaotic dynamics and random polynomials
    • [BBL] Bogomolny, E., Bohigas, O. and Leboeuf, P.: Quantum chaotic dynamics and random polynomials. J. Stat. Phys. 85, 639-679 (1996)
    • (1996) J. Stat. Phys. , vol.85 , pp. 639-679
    • Bogomolny, E.1    Bohigas, O.2    Leboeuf, P.3
  • 4
    • 0003340015 scopus 로고
    • The spectral theory of toeplitz operators
    • Princeton, NJ: Princeton Univ. Press
    • [BG] Boulet de Monvel, L. and Guillemin, V.: The Spectral Theory of Toeplitz Operators. Ann. Math. Studies 99, Princeton, NJ: Princeton Univ. Press, 1981
    • (1981) Ann. Math. Studies , vol.99
    • Boulet De Monvel, L.1    Guillemin, V.2
  • 5
    • 0030293308 scopus 로고    scopus 로고
    • Symplectic submanifols and almost complex geometry
    • [D] Donaldson, S.: Symplectic submanifols and almost complex geometry. J. Diff. Geom. 44, 666-705 (1996)
    • (1996) J. Diff. Geom. , vol.44 , pp. 666-705
    • Donaldson, S.1
  • 6
    • 0001194030 scopus 로고
    • On the distribution of roots of polynomials
    • [ET] Erdos, P. and Turan, P.: On the distribution of roots of polynomials. Ann. Math. 51, 105-119 (1950)
    • (1950) Ann. Math. , vol.51 , pp. 105-119
    • Erdos, P.1    Turan, P.2
  • 7
    • 0000819285 scopus 로고
    • Complex dynamics in higher dimensions, II
    • Modern methods in Complex Analysis, Princeton, NJ, Princeton, NJ: Princeton Univ. Press
    • [FS] Fornaess, J.E. and Sibony, N.: Complex dynamics in higher dimensions, II. Modern methods in Complex Analysis, Princeton, NJ, 1992, Ann. of Math. Stud. 137, Princeton, NJ: Princeton Univ. Press, 1995, pp. 135-182
    • (1992) Ann. of Math. Stud. , vol.137 , pp. 135-182
    • Fornaess, J.E.1    Sibony, N.2
  • 8
    • 0000321857 scopus 로고
    • Über modifikationen und exzeptionelle analytische Mengen
    • [Gr] Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Annalen 146, 331-368 (1962)
    • (1962) Math. Annalen , vol.146 , pp. 331-368
    • Grauert, H.1
  • 10
    • 21344460437 scopus 로고    scopus 로고
    • Chaotic analytic zero points: Exact statistics for those of a random spin state
    • [Ha] Hannay, J.H.: Chaotic analytic zero points: Exact statistics for those of a random spin state. J. Phys. A: Math. Gen. 29, 101-105 (1996)
    • (1996) J. Phys. A: Math. Gen. , vol.29 , pp. 101-105
    • Hannay, J.H.1
  • 11
    • 0003284896 scopus 로고
    • The analysis of linear partial differential operators
    • New York: Springer-Verlag
    • [Ho] Hörmander, L.: The Analysis of Linear Partial Differential Operators. Grund. Math. Wiss. bf256, New York: Springer-Verlag, 1983
    • (1983) Grund. Math. Wiss. , vol.BF256
    • Hörmander, L.1
  • 12
    • 42549171482 scopus 로고
    • On the average number of real roots of a random algebraic equation
    • [Ka] Kac, M.: On the average number of real roots of a random algebraic equation. Bull. Am. Math. Soc. 49, 314-320 (1943)
    • (1943) Bull. Am. Math. Soc. , vol.49 , pp. 314-320
    • Kac, M.1
  • 14
    • 0343861097 scopus 로고    scopus 로고
    • Universal fluctuations of zeros of chaotic wavefunctions
    • [LS] Leboeuf, P. and Shukla, P.: Universal fluctuations of zeros of chaotic wavefunctions. J. Phys. A: Math. Gen. 29, 4827-4835 (1996)
    • (1996) J. Phys. A: Math. Gen. , vol.29 , pp. 4827-4835
    • Leboeuf, P.1    Shukla, P.2
  • 15
    • 0000496135 scopus 로고
    • On the number of real roots of random algebraic equations I, II, III
    • [LO] Littlewood, J. and Offord, A.: On the number of real roots of random algebraic equations I, II, III. J. London Math. Soc. 13, 288-295 (1938); Proc. Camb. Phil. Soc. 35, 133-148 (1939); Math. Shorn. 12, 277-286 (1943)
    • (1938) J. London Math. Soc. , vol.13 , pp. 288-295
    • Littlewood, J.1    Offord, A.2
  • 16
    • 84958737079 scopus 로고
    • [LO] Littlewood, J. and Offord, A.: On the number of real roots of random algebraic equations I, II, III. J. London Math. Soc. 13, 288-295 (1938); Proc. Camb. Phil. Soc. 35, 133-148 (1939); Math. Shorn. 12, 277-286 (1943)
    • (1939) Proc. Camb. Phil. Soc. , vol.35 , pp. 133-148
  • 17
    • 0000496135 scopus 로고
    • [LO] Littlewood, J. and Offord, A.: On the number of real roots of random algebraic equations I, II, III. J. London Math. Soc. 13, 288-295 (1938); Proc. Camb. Phil. Soc. 35, 133-148 (1939); Math. Shorn. 12, 277-286 (1943)
    • (1943) Math. Shorn. , vol.12 , pp. 277-286
  • 19
    • 0002324871 scopus 로고    scopus 로고
    • Value distribution for sequences of rational mappings and complex dynamics
    • [RSh] Russakovskii, A. and Shiffman, B.: Value distribution for sequences of rational mappings and complex dynamics. Indiana Univ. Math. J. 46, 897-932 (1997)
    • (1997) Indiana Univ. Math. J. , vol.46 , pp. 897-932
    • Russakovskii, A.1    Shiffman, B.2
  • 20
    • 0008997559 scopus 로고
    • Equidistribution for sequences of polynomial mappings
    • [RSo] Russakovskii, A. and Sodin, M.: Equidistribution for sequences of polynomial mappings. Indiana Univ. Math. J. 44, 851-882 (1995)
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 851-882
    • Russakovskii, A.1    Sodin, M.2
  • 21
    • 21844506265 scopus 로고
    • The complex zeros of random polynomials
    • [SV] Shepp, L.A. and Vanderbei, R.J.: The complex zeros of random polynomials. Trans. Am. Math. Soc. 347, 4365-4384 (1995)
    • (1995) Trans. Am. Math. Soc. , vol.347 , pp. 4365-4384
    • Shepp, L.A.1    Vanderbei, R.J.2
  • 22
    • 0008985226 scopus 로고
    • Applications of geometric measure theory to value distribution theory for meromorphic maps
    • New York: Marcel-Dekker
    • [Sh] Shiffman, B.: Applications of geometric measure theory to value distribution theory for meromorphic maps. Value-Distribution Theory, Part A. New York: Marcel-Dekker, 1974, pp. 63-96
    • (1974) Value-Distribution Theory, Part A , pp. 63-96
    • Shiffman, B.1
  • 23
    • 0003221655 scopus 로고
    • Vanishing theorems on complex manifolds
    • Boston: Birkhäuser
    • [SS] Shiffman, B. and Sommese, A.J.: Vanishing Theorems on Complex Manifolds. Progress in Math. 56, Boston: Birkhäuser, 1985
    • (1985) Progress in Math. , vol.56
    • Shiffman, B.1    Sommese, A.J.2
  • 24
    • 0001022947 scopus 로고
    • Ergodic properties of eigenfunctions
    • [Shn1] Shnirelman, A.I.: Ergodic properties of eigenfunctions. Usp. Mat. Nauk. 29/6, 181-182 (1974)
    • (1974) Usp. Mat. Nauk. , vol.29 , Issue.6 , pp. 181-182
    • Shnirelman, A.I.1
  • 25
    • 0008995315 scopus 로고
    • On the asymptotic properties of eigenfunctions in the region of chaotic motion
    • Addendum to V. F. Lazutkin, New York: Springer-Verlag
    • [Shn2] Shnirelman, A.I.: On the asymptotic properties of eigenfunctions in the region of chaotic motion. Addendum to V. F. Lazutkin, KAM Theory and Semiclassical Approximations to Eigenfunctions, New York: Springer-Verlag, 1993
    • (1993) KAM Theory and Semiclassical Approximations to Eigenfunctions
    • Shnirelman, A.I.1
  • 26
    • 5044221652 scopus 로고
    • Value distribution of sequences of rational mappings
    • Entire and Subharmonic Functions, B. Ya. Levin, ed.
    • [So] Sodin, M.L.: Value distribution of sequences of rational mappings. Entire and Subharmonic Functions, B. Ya. Levin, ed., Advances in Soviet Math. 11, 1992
    • (1992) Advances in Soviet Math. , vol.11
    • Sodin, M.L.1
  • 27
    • 0003151792 scopus 로고
    • On a set of polarized Kahler metrics on algebraic manifolds
    • [T] Tian, G.: On a set of polarized Kahler metrics on algebraic manifolds. J. Diff. Geometry 32, 99-130 (1990)
    • (1990) J. Diff. Geometry , vol.32 , pp. 99-130
    • Tian, G.1
  • 28
    • 0001264939 scopus 로고    scopus 로고
    • L∞ norms and quantum ergodicity on the sphere
    • [V] VanderKam, J.M.: L∞ norms and quantum ergodicity on the sphere. Int. Math. Res. Notices 7. 329-347 (1997)
    • (1997) Int. Math. Res. Notices , vol.7 , pp. 329-347
    • Vanderkam, J.M.1
  • 30
    • 0002492588 scopus 로고
    • Quantum ergodicity on the sphere
    • [Z1] Zelditch, S.: Quantum ergodicity on the sphere. Commun. Math. Phys. 146, 61-71 (1992)
    • (1992) Commun. Math. Phys. , vol.146 , pp. 61-71
    • Zelditch, S.1
  • 31
    • 0009074255 scopus 로고    scopus 로고
    • A random matrix model for quantum mixing
    • [Z2] Zelditch, S.: A random matrix model for quantum mixing. Int. Math. Res. Notices 3, 115-137 (1996)
    • (1996) Int. Math. Res. Notices , vol.3 , pp. 115-137
    • Zelditch, S.1
  • 32
    • 0031513741 scopus 로고    scopus 로고
    • Index and dynamics of quantized contact transformations
    • [Z3] Zelditch, S.: Index and dynamics of quantized contact transformations. Annales de l'Institut Fourier (Grenoble) 47, 305-363 (1997)
    • (1997) Annales de l'Institut Fourier (Grenoble) , vol.47 , pp. 305-363
    • Zelditch, S.1
  • 33
    • 0000647318 scopus 로고    scopus 로고
    • Szegö kernels and a theorem of Tian
    • [Z4] Zelditch, S.: Szegö kernels and a theorem of Tian: Int. Math. Res. Notices 6, 317-331 (1998)
    • (1998) Int. Math. Res. Notices , vol.6 , pp. 317-331
    • Zelditch, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.