Geodesic
Mean-field models in the theory of random media. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 281-290 
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/
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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.

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