Behavior of some Wiener integrals as $t\to\infty$ and the density of states of Schrödinger equations with random potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 1, pp. 88-95
Cet article a éte moissonné depuis la source Math-Net.Ru
The first terms in the asymptotics for $t\to\infty$ of Wiener integrals over the trajectories of $D$-dimensional Brownian motion are derived in the cases when integrated functional has the form $\left<\exp\left\{-\int\limits_0^t q(x(s))\,ds\right\}\right>$ where $q(x)$ is the Gaussian random field or the Poisson field of the form $\sum\limits_j V(x-x_j)$ with showly decreasing positive V(x) or negative $V(x)=(V_0/|x|^\alpha)(1+o(1))$, $|x|\to\infty$, $d<\alpha, and $0>\min V(x)=V(0)>-\infty$ respectively. These results are used to obtain asymptotic formulas for density of states on the left end of the spectrum of Schrödinger equation with such random fields as the potentials.
@article{TMF_1977_32_1_a6,
author = {L. A. Pastur},
title = {Behavior of some {Wiener} integrals as $t\to\infty$ and the density of states of {Schr\"odinger} equations with random potential},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {88--95},
year = {1977},
volume = {32},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1977_32_1_a6/}
}
TY - JOUR AU - L. A. Pastur TI - Behavior of some Wiener integrals as $t\to\infty$ and the density of states of Schrödinger equations with random potential JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1977 SP - 88 EP - 95 VL - 32 IS - 1 UR - http://geodesic.mathdoc.fr/item/TMF_1977_32_1_a6/ LA - ru ID - TMF_1977_32_1_a6 ER -
%0 Journal Article %A L. A. Pastur %T Behavior of some Wiener integrals as $t\to\infty$ and the density of states of Schrödinger equations with random potential %J Teoretičeskaâ i matematičeskaâ fizika %D 1977 %P 88-95 %V 32 %N 1 %U http://geodesic.mathdoc.fr/item/TMF_1977_32_1_a6/ %G ru %F TMF_1977_32_1_a6
L. A. Pastur. Behavior of some Wiener integrals as $t\to\infty$ and the density of states of Schrödinger equations with random potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 1, pp. 88-95. http://geodesic.mathdoc.fr/item/TMF_1977_32_1_a6/
[1] M. Donsker, S. Varadhan, Commun. Pure and Appl. Mathem., 28 (1975), 525 | DOI | MR | Zbl
[2] M. Kats, Veroyatnost i smezhnye voprosy v fizike, «Mir», 1965 | Zbl
[3] D. Ryuel, Statisticheskaya mekhanika, «Mir», 1971
[4] S. M. Rytov, Vvedenie v statisticheskuyu radiofiziku, «Nauka», 1965
[5] L. A. Pastur, Funkts. analiz i ego prim., 6 (1972), 93 | MR | Zbl
[6] L. A. Pastur, TMF, 6 (1971), 415 | MR | Zbl