메뉴 건너뛰기




Volumn 9, Issue 4, 2006, Pages 291-333

The canopy graph and level statistics for random operators on trees

Author keywords

Absolutely continuous spectrum; Anderson localization; Canopy graph; Level statistics; Random operators; Singular continuous spectrum

Indexed keywords


EID: 34249675427     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11040-007-9018-3     Document Type: Article
Times cited : (65)

References (44)
  • 1
    • 21144468416 scopus 로고
    • Analyticity of the density of states in the Anderson model on the Bethe lattice
    • Acosta, V., Klein, A.: Analyticity of the density of states in the Anderson model on the Bethe lattice. J. Statist. Phys. 69, 277-305 (1992)
    • (1992) J. Statist. Phys , vol.69 , pp. 277-305
    • Acosta, V.1    Klein, A.2
  • 2
    • 51249162086 scopus 로고
    • Density of states in spectral geometry
    • Adachi, T., Sunada, T.: Density of states in spectral geometry. Comment. Math. Helv. 68, 480-493 (1993)
    • (1993) Comment. Math. Helv , vol.68 , pp. 480-493
    • Adachi, T.1    Sunada, T.2
  • 3
    • 21344491724 scopus 로고
    • Localization at large disorder and at extreme energies: An elementary derivation
    • Aizenman, M., Molchanov, S.: Localization at large disorder and at extreme energies: an elementary derivation. Comm. Math. Phys. 157, 245-278 (1993)
    • (1993) Comm. Math. Phys , vol.157 , pp. 245-278
    • Aizenman, M.1    Molchanov, S.2
  • 4
    • 0001324593 scopus 로고
    • Localization at weak disorder: Some elementary bounds
    • Aizenman, M.: Localization at weak disorder: some elementary bounds. Rev. Math. Phys. 6, 1163-1182 (1994)
    • (1994) Rev. Math. Phys , vol.6 , pp. 1163-1182
    • Aizenman, M.1
  • 5
    • 33747884265 scopus 로고    scopus 로고
    • Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs
    • Aizenman, M., Sims, R., Warzel, S.: Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Probab. Theory Related Fields 136, 363-394 (2006)
    • (2006) Probab. Theory Related Fields , vol.136 , pp. 363-394
    • Aizenman, M.1    Sims, R.2    Warzel, S.3
  • 6
    • 33645979029 scopus 로고    scopus 로고
    • Absolutely continuous spectra of quantum tree graphs with weak disorder
    • Aizenman, M., Sims, R., Warzel, S.: Absolutely continuous spectra of quantum tree graphs with weak disorder. Comm. Math. Phys. 264, 371-389 (2006)
    • (2006) Comm. Math. Phys , vol.264 , pp. 371-389
    • Aizenman, M.1    Sims, R.2    Warzel, S.3
  • 7
    • 0034555445 scopus 로고    scopus 로고
    • A Mourre estimate for a Schrödinger operator on a binary tree
    • Allard, C., Froese, R.: A Mourre estimate for a Schrödinger operator on a binary tree. Rev. Math. Phys. 12, 1655-1667 (2000)
    • (2000) Rev. Math. Phys , vol.12 , pp. 1655-1667
    • Allard, C.1    Froese, R.2
  • 8
    • 0001258717 scopus 로고
    • Repulsion of energy levels and conductivity of metal samples
    • Altshuler, B., Shklovski, B.I.: Repulsion of energy levels and conductivity of metal samples. Sov. Phys. JETP 64, 127-135 (1986)
    • (1986) Sov. Phys. JETP , vol.64 , pp. 127-135
    • Altshuler, B.1    Shklovski, B.I.2
  • 9
    • 0035532622 scopus 로고    scopus 로고
    • Random incidence matrices: Moments of the spectral density
    • Bauer, M., Golinelli, O.: Random incidence matrices: moments of the spectral density. J. Statist. Phys. 103, 301-337 (2000)
    • (2000) J. Statist. Phys , vol.103 , pp. 301-337
    • Bauer, M.1    Golinelli, O.2
  • 11
    • 0042181128 scopus 로고
    • On the comparison of transcendentals, with certain application to the theory of definite integrals
    • Boole, G.: On the comparison of transcendentals, with certain application to the theory of definite integrals. Philos. Trans. Roy. Soc. London Ser. A 147, 780 (1857)
    • (1857) Philos. Trans. Roy. Soc. London Ser. A , vol.147 , pp. 780
    • Boole, G.1
  • 12
    • 34249738369 scopus 로고    scopus 로고
    • Breuer, J.: Singular continuous and dense point spectrum for sparse trees with finite dimensions. Available at math.SP/0608159 (2006)
    • Breuer, J.: Singular continuous and dense point spectrum for sparse trees with finite dimensions. Available at math.SP/0608159 (2006)
  • 13
    • 0002362803 scopus 로고
    • Anderson localization for Bernoulli and other singular potentials
    • Carmona, R., Klein, A., Martinelli, F.: Anderson localization for Bernoulli and other singular potentials. Comm. Math. Phys. 108, 41-66 (1987)
    • (1987) Comm. Math. Phys , vol.108 , pp. 41-66
    • Carmona, R.1    Klein, A.2    Martinelli, F.3
  • 15
    • 34249723533 scopus 로고    scopus 로고
    • del Rio, R., Simon, B., Stolz, G.: Stability of spectral types for Sturm-Liouville operators. Math. Res. Lett. 1, 437-.450 (1994)
    • del Rio, R., Simon, B., Stolz, G.: Stability of spectral types for Sturm-Liouville operators. Math. Res. Lett. 1, 437-.450 (1994)
  • 16
    • 0001067228 scopus 로고
    • Appearance of purely singular continuous spectrum in a class of random Schrödinger operators
    • Delyon, F.: Appearance of purely singular continuous spectrum in a class of random Schrödinger operators. J. Statist. Phys. 40, 621-630 (1985)
    • (1985) J. Statist. Phys , vol.40 , pp. 621-630
    • Delyon, F.1
  • 17
    • 36149045549 scopus 로고
    • One-dimensional wave equations in disordered media
    • Delyon, F., Kunz, H., Souillard, B.: One-dimensional wave equations in disordered media. J. Phys. A, Math. Gen. 16, 25-42 (1983)
    • (1983) J. Phys. A, Math. Gen , vol.16 , pp. 25-42
    • Delyon, F.1    Kunz, H.2    Souillard, B.3
  • 18
    • 0036386544 scopus 로고    scopus 로고
    • The spectral measure of certain elements of the complex group ring of a wreath product
    • Dicks, W., Schick, T.: The spectral measure of certain elements of the complex group ring of a wreath product. Geom. Dedicata 93, 121-134 (2001)
    • (2001) Geom. Dedicata , vol.93 , pp. 121-134
    • Dicks, W.1    Schick, T.2
  • 20
    • 0003072651 scopus 로고
    • Spectral density singularities, level statistics, and localization in a sparse random matrix ensemble
    • Evangelou, S.N., Economou, E.N.: Spectral density singularities, level statistics, and localization in a sparse random matrix ensemble. Phys. Rev. Lett. 68, 361-364 (1992)
    • (1992) Phys. Rev. Lett , vol.68 , pp. 361-364
    • Evangelou, S.N.1    Economou, E.N.2
  • 21
    • 21144466780 scopus 로고
    • A numerical study of sparse random matrices
    • Evangelou, S.N.: A numerical study of sparse random matrices. J. Statist. Phys. 69, 361-364 (1992)
    • (1992) J. Statist. Phys , vol.69 , pp. 361-364
    • Evangelou, S.N.1
  • 23
    • 33751082634 scopus 로고    scopus 로고
    • Absolutely continuous spectrum for the Anderson model on a tree: A geometric proof of Klein's theorem
    • Froese, R., Hasler, D., Spitzer, W.: Absolutely continuous spectrum for the Anderson model on a tree: a geometric proof of Klein's theorem. Comm. Math. Phys. 269, 239-257 (2007)
    • (2007) Comm. Math. Phys , vol.269 , pp. 239-257
    • Froese, R.1    Hasler, D.2    Spitzer, W.3
  • 24
    • 34249739465 scopus 로고    scopus 로고
    • Graf, G.M., Vaghi, A.: A remark on an estimate by Minami. Available at math-ph/0604033 (2006).
    • Graf, G.M., Vaghi, A.: A remark on an estimate by Minami. Available at math-ph/0604033 (2006).
  • 25
    • 0003231591 scopus 로고    scopus 로고
    • The lamplighter group as a group generated by a 2-state automaton and its spectrum
    • Grigorchuk, R.I., Zuk, A.: The lamplighter group as a group generated by a 2-state automaton and its spectrum. Geom. Dedicata 87, 209-244 (2001)
    • (2001) Geom. Dedicata , vol.87 , pp. 209-244
    • Grigorchuk, R.I.1    Zuk, A.2
  • 28
    • 33747889674 scopus 로고
    • The Anderson metal-insulator transition on the Bethe lattice
    • Iagolnitzer, D, ed, Paris, France, July 18-23, International Press, Cambridge, MA
    • Klein, A.: The Anderson metal-insulator transition on the Bethe lattice. In: Iagolnitzer, D. (ed.), Proceedings of the XIth International Congress on Mathematical Physics, Paris, France, July 18-23, 1994. International Press, Cambridge, MA (1995)
    • (1994) Proceedings of the XIth International Congress on Mathematical Physics
    • Klein, A.1
  • 29
    • 0000120387 scopus 로고    scopus 로고
    • Extended states in the Anderson model on the Bethe lattice
    • Klein, A.: Extended states in the Anderson model on the Bethe lattice. Adv. Math. 133, 163-184 (1998)
    • (1998) Adv. Math , vol.133 , pp. 163-184
    • Klein, A.1
  • 30
    • 0001097161 scopus 로고
    • Sur le spectre des operateurs aux difference finies aleatoire
    • Kunz, H., Souillard, B.: Sur le spectre des operateurs aux difference finies aleatoire. Comm. Math. Phys. 78, 201-246 (1980)
    • (1980) Comm. Math. Phys , vol.78 , pp. 201-246
    • Kunz, H.1    Souillard, B.2
  • 31
    • 0347963946 scopus 로고    scopus 로고
    • Periodic orbit theory and spectral statistics for quantum graphs
    • Kottos, T., Smilansky, U.: Periodic orbit theory and spectral statistics for quantum graphs. Ann. Physics 274, 76-124 (1999)
    • (1999) Ann. Physics , vol.274 , pp. 76-124
    • Kottos, T.1    Smilansky, U.2
  • 32
    • 34249766319 scopus 로고
    • Weak disorder expansion for the Anderson model on a tree
    • Miller, J.D., Derrida, B.: Weak disorder expansion for the Anderson model on a tree. J. Statist. Phys. 75, 357-388 (1993)
    • (1993) J. Statist. Phys , vol.75 , pp. 357-388
    • Miller, J.D.1    Derrida, B.2
  • 33
    • 0030553788 scopus 로고    scopus 로고
    • Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
    • Minami, N.: Local fluctuation of the spectrum of a multidimensional Anderson tight binding model. Comm. Math. Phys. 177, 709-725 (1996)
    • (1996) Comm. Math. Phys , vol.177 , pp. 709-725
    • Minami, N.1
  • 34
    • 36149035179 scopus 로고
    • Universality of the level correlation function of sparse random matrices
    • Mirlin, A.D., Fyodorov, Y.V.: Universality of the level correlation function of sparse random matrices. J. Phys. A, Math. Gen. 24, 2273-2286 (1991)
    • (1991) J. Phys. A, Math. Gen , vol.24 , pp. 2273-2286
    • Mirlin, A.D.1    Fyodorov, Y.V.2
  • 35
    • 5544291378 scopus 로고
    • The local structure of the spectrum of the one-dimensional Schrödinger operator
    • Molchanov, S.A.: The local structure of the spectrum of the one-dimensional Schrödinger operator. Comm. Math. Phys. 78, 429-446 (1981)
    • (1981) Comm. Math. Phys , vol.78 , pp. 429-446
    • Molchanov, S.A.1
  • 37
    • 21344446681 scopus 로고    scopus 로고
    • Simon, B.: Operators with singular continuous spectrum, IV: Graph Laplacians and Laplace-Beltrami operators. Proc. Amer. Math. Soc. 124, 1177-1182 (1996)
    • Simon, B.: Operators with singular continuous spectrum, IV: Graph Laplacians and Laplace-Beltrami operators. Proc. Amer. Math. Soc. 124, 1177-1182 (1996)
  • 38
    • 84990576488 scopus 로고
    • Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians
    • Simon, B., Wolff, T.: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Comm. Pure Appl. Math. 39, 75-90 (1986)
    • (1986) Comm. Pure Appl. Math , vol.39 , pp. 75-90
    • Simon, B.1    Wolff, T.2
  • 39
    • 0001664226 scopus 로고
    • Statistics of spectra of disordered systems near the metal-insulator transition
    • Shklovskii, B.I., Shapiro, B., Sears, B.R., Lambrianides, P., Shore, H.B.: Statistics of spectra of disordered systems near the metal-insulator transition. Phys. Rev. B 47, 11487-11490 (1993)
    • (1993) Phys. Rev. B , vol.47 , pp. 11487-11490
    • Shklovskii, B.I.1    Shapiro, B.2    Sears, B.R.3    Lambrianides, P.4    Shore, H.B.5
  • 41
    • 84990582138 scopus 로고
    • Lifshitz tail and Wiener sausage on hyperbolic space
    • Sznitman, A.-S.: Lifshitz tail and Wiener sausage on hyperbolic space. Comm. Pure Appl. Math. 17, 1033-1065 (1989)
    • (1989) Comm. Pure Appl. Math , vol.17 , pp. 1033-1065
    • Sznitman, A.-S.1
  • 42
    • 84990627117 scopus 로고
    • Lifshitz tail on hyperbolic space: Neumann conditions
    • Sznitman, A.-S.: Lifshitz tail on hyperbolic space: Neumann conditions. Comm. Pure Appl. Math. 18, 1-30 (1990)
    • (1990) Comm. Pure Appl. Math , vol.18 , pp. 1-30
    • Sznitman, A.-S.1
  • 43
    • 0002037112 scopus 로고
    • Bounds on the density of states in disordered systems
    • Wegner, F.: Bounds on the density of states in disordered systems. Z. Phys. B 44, 9-15 (1981)
    • (1981) Z. Phys. B , vol.44 , pp. 9-15
    • Wegner, F.1
  • 44
    • 0005282985 scopus 로고    scopus 로고
    • Random walks on infinite graphs and groups
    • Cambridge University Press, Cambridge
    • Woess, W.: Random walks on infinite graphs and groups. In: Cambridge Tracts in Mathematics, vol. 138. Cambridge University Press, Cambridge (2000)
    • (2000) Cambridge Tracts in Mathematics , vol.138
    • Woess, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.