×
Grenkova, L. N.; Molchanov, S. A.; Sudarev, Yu. N.

On the basic states of one-dimensional disordered structures. (English) Zbl 0517.60072

Commun. Math. Phys. 90, 101-123 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0517.60072

Cited in 15 Documents

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
35J10 Schrödinger operator, Schrödinger equation
60G10 Stationary stochastic processes

Keywords:

limit probability distribution of eigenvalues; random Schrödinger operator
Cite Review PDF
Full Text: DOI

References:

[1] Pastur, L.A.: The spectra of the random self-adjointness operators. Usp. Mat. Nauk28, 3–64 (1969), (1973). English transl. in Russian Math. Surv.28, (1973)
[2] Kozlov, S.M.: The averaging of the random operators. Mat. Sb. 109 (151) 188–202 (1979)
[3] Lipšic, I.M., Gredeskul, S.A., Pastur, L.A.: An introduction to disordered system theory. Moskva: Nauka 1982
[4] Molčanov, S.A.: On the nature of the eigenfunctions of one-dimensional disordered structures. Izv. Akad. Nauk SSSR42, 70–103 (1978); English transl. in Math. SSSR Izv.12, (1978)
[5] Molčanov, S.A.: The local structure of the spectrum of the Random one-dimensional Schrödinger operator. Commun. Math. Phys.78, 429–446 (1981) · Zbl 0449.60049 · doi:10.1007/BF01942333
[6] Malkin, V.M.: The distribution of the distances between the energetic levels of the particle in one-dimensional random field. Preprint 81-49, IIAF SO Akad. Nauk SSSR, Novosibirsk, 1981
[7] Casati, G., Valz-Gris, F., Guarniery, I.: On the connection between quantization of nonintegrable systems and statistical theory of spectra. Let. Nuovo Cimento28, 279 (1980) · doi:10.1007/BF02798790
[8] Gordin, M.I., Lifšic, B.A.: The central limit theorem for Markov stationary processes. Dokl. Akad. Nauk SSSR239, 766–767 (1978)
[9] Ibragimov, J.A., Linnik, Ju.V.: Independent and stationary connected variables. Moskva: Nauka 1965 · Zbl 0154.42201
[10] Billingsley, P.: Convergence of probability measures. New York: Wiley 1968 · Zbl 0172.21201
[11] Narimanjan, S.M.: The central limit theorem for random walk on the circle. Dokl. Akad. Nauk Arm. SSSR64, 129–136 (1977)
[12] Anshelevich, V.V., Vologodskii, A.V.: Laplace operator and Random walk on one-dimensional nonhomogeneous lattice. J. Stat. Phys.25, 419–430 (1981) · Zbl 0512.60059 · doi:10.1007/BF01010797
[13] Anshelevich, V.V., Khanin, K.M., Sinai, Ya.G.: Symmetric Random walks in Random environments. Commun. Math. Phys.85, 449–470 (1982) · Zbl 0512.60058 · doi:10.1007/BF01208724
[14] Friedrichs, K.O.: Perturbation of spectra in Hilbert space. Providence, Rhode Island: Am. Math. Society, 1965 · Zbl 0142.11001
[15] Feller, W.: An introduction to probability theory and its applications. New York: Wiley 1966 · Zbl 0138.10207
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.