Mean-field models in the theory of random media. II

A study is made of a stationary random medium described by the evolution equation $\partial\psi/\partial t=\varkappa\overline\Delta_V+\xi(\mathbf x)\psi$ where $\overline\Delta_V$ is the operator of mean-field diffusion in the volume $V\subset\mathbf Z^d$, $\xi(\mathbf x),\mathbf x\in V$, are independent random variables with normal distribution $\mathbf N(0,\sigma^2)$. A study is made of the asymptotic behavior of the solution $\psi(\mathbf x,t)$ and its statistical moments $m_p(\mathbf x,t)=\langle\psi^p(\mathbf x,t)\rangle$, $p=1,2,\dots$, as $t\to\infty$, $|V|\to\infty$. The paper continues the earlier [1].