Mean-field models in~the theory of~random media.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 281-290
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It is the first in the series of works treating the problems of the theory of random media on the basis of the mean field (nonlocal) diffusion approximation with the corresponding operator $\overline\Delta_V$, $V\subset\mathbf Z^d$. The general introduction to the whole cycle is presented including a brief survey of problems in the theory of random media. The localization problem for the operator $H_V=\overline\Delta_V+\xi(x)$ is also considered, where $\{\xi(x)\}$ are i. i. d. continious random variables, $|V|\to\infty$. It is proved that the localization in the average (uniformly in $V$) takes place.
@article{TMF_1989_81_2_a12,
author = {L. V. Bogachev and S. A. Molchanov},
title = {Mean-field models in~the theory of~random {media.~I}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {281--290},
publisher = {mathdoc},
volume = {81},
number = {2},
year = {1989},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a12/}
}
L. V. Bogachev; S. A. Molchanov. Mean-field models in~the theory of~random media.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 281-290. http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a12/