Geodesic
The structure of eigenfunctions of one-dimensional unordered structures
Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 69-101.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this work it is shown that all the eigenfunctions of the one-dimensional random Schröger operator $H=-d^2/dt^2+q(t,\omega)$, $t\in R^1$, with random potential $q(t,\omega)$, $\omega\in\Omega$, of Markov type decrease exponentially with probability 1. This confirms an old conjecture of N. F. Mott which has been discussed many times in the physics literature. Bibliography: 14 titles. 
@article{IM2_1978_12_1_a3,
     author = {S. A. Molchanov},
     title = {The structure of eigenfunctions of one-dimensional unordered structures},
     journal = {Izvestiya. Mathematics },
     pages = {69--101},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a3/}
}
TY  - JOUR
AU  - S. A. Molchanov
TI  - The structure of eigenfunctions of one-dimensional unordered structures
JO  - Izvestiya. Mathematics 
PY  - 1978
SP  - 69
EP  - 101
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a3/
LA  - en
ID  - IM2_1978_12_1_a3
ER  - 
%0 Journal Article
%A S. A. Molchanov
%T The structure of eigenfunctions of one-dimensional unordered structures
%J Izvestiya. Mathematics 
%D 1978
%P 69-101
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a3/
%G en
%F IM2_1978_12_1_a3
S. A. Molchanov. The structure of eigenfunctions of one-dimensional unordered structures. Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 69-101. http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a3/

[1] Mott N., Elektrony v neuporyadochennykh strukturakh, Mir, M., 1969

[2] Lifshits I. M., “O strukture energeticheskogo spektra i kvantovykh sostoyanii neuporyadochennykh kondensirovannykh sistem”, Uspekhi fiz. nauk, 83:4 (1964), 617 | Zbl

[3] Halperin B. I., “Properties of a particle in a one-dimensional random potential”, Adv. in Chem. Phys., 13 (1967), 123–178 | DOI

[4] Pastur L. A., “Spektry sluchainykh operatorov”, Uspekhi matem. nauk, 28:3 (1977), 3–64 | MR

[5] Goldsheid I. Ya., Molchanov S. A., Pastur L. A., “Sluchainyi odnomernyi operator Shredingera imeet chisto tochechnyi spektr”, Funktsion. analiz, 11:1 (1977), 1–10 | MR | Zbl

[6] Goldsheid I. Ya., Molchanov S. A., “O probleme Motta”, Dokl. AN SSSR, 230:4 (1976), 671–674

[7] Vul E. B., O sluchainom operatore Shredingera, Tr. III Konferentsii po teorii informatsii, Leningrad, 1976

[8] Makkin G., Stokhasticheskie integraly, Mir, M., 1972 | MR

[9] Bekkenbakh E., Bellman R., Neravenstva, Mir, M., 1965 | MR

[10] Strook P., Varadhan S. R. S., “On degenerated elliptic-parabolic operators of second order and their associated diffusions”, Comm. Pure Appl. Math., 25:6 (1972), 651–713 | DOI | MR

[11] Sonin I. M., “Ob odnom klasse vyrozhdayuschikhsya diffuzionnykh protsessov”, Teor. veroyatnostei i ee primeneniya, 12:3 (1967), 540–547 | MR | Zbl

[12] Danford N., Shvarts Dzh. T., Lineinye operatory (spektralnaya teoriya), Mir, M., 1966

[13] Furstenberg H., “Random products”, Trans. Amer. Math. Soc., 108 (1963), 377 | DOI | MR | Zbl

[14] Kramer G., Lidbetter M., Statsionarnye sluchainye protsessy, Mir, M., 1969