all exponentials in are independent and $v$ and $D$ are well-defined parameters for all temperatures above the transition temperature $T_0=U_0/k$. For this reason there is a general belief that for the nondispersive regime $\varkappa < 1$ transport could be rather accurately described by the diffusion equation with well-defined average velocity $v$ and diffusivity $D$. In this paper we study the nondispersive regime in details and show that for the correlated random energy landscape the picture is more complicated and diffusivity $D$ demonstrates quite nontrivial behavior.

Gaussian representation for the exponentially distributed random energy $U(x)$ {#Gauss}
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A suitable method to introduce spatial correlation in the exponentially distributed random energy landscape has been suggested in Ref. . There is a well known representation for the exponentially distributed random variable which employs two auxiliary independent identically distributed random Gaussian variables $X$ and $Y$ having zero mean and unit variance $\sigma^2=1$. If $$U=-\frac{1}{2}U_0\left(X^2+Y^2\right),
\label{U-XY_a}$$ then $U$ is distributed according to [@Devroye-book]. If $X(x)$ and $Y(x)$ are Gaussian random fields with correlation functions $c_X(x)$ and $c_Y(x)$, then the resulting distribution of $U(x)$ is spatially correlated, too. Using this trick the averaging over $U(x)$ is replaced by the averaging over $X(x)$ and $Y(x)$.

This approach 