consider the simplest case $c_X(x)=c_Y(x)=c(x)$, possible generalizations may be found in Ref. . We assume also that our system is isotropic, so $c(x)=c(-x)$. To calculate $Z_4(x,y,z)$, we need the analogous 4-point distribution $$\label{P4}
P_4(X_i,c)=\frac{1}{(2\pi)^2\sqrt{\det \textbf{G}^{-1}}}\exp\left[
-\frac{1}{2}\sum\limits_{i,j=1}^4 X_i X_j G_{ij}\right],$$ where the elements of the symmetric $4\times 4$ matrix $\textbf{G}^{-1}$ are $G^{-1}_{ij}=c(x_i-x_j)$. Here $x_1=x+y$, $x_2=x$, $x_3=0$, and $x_4=-z$. Performing averaging over $X_i$, $Y_i$ using distribution (\[P4\]) we obtain for the correlation function $Z_4(x,y,z)$ $$Z_4(x,y,z)=\frac{1}{\det \textbf{T}}, \hskip10pt \textbf{T}= \textbf{G}^{-1}\widetilde{\textbf{G}},
\label{Z4}$$ where matrix $\widetilde{\textbf{G}}$ differs from $\textbf{G}$ only in diagonal elements $\widetilde{G}_{ij}=G_{ij}+(-1)^{i-1}\varkappa\delta_{ij}$.

Matrix $\textbf{G}^{-1}$ has the structure $$\textbf{G}^{-1}=
\begin{pmatrix}
    \textbf{A}       & \textbf{C} \\
    \textbf{C}'       & \textbf{B}
\end{pmatrix},
\label{Ginf}$$ where $\textbf{A}$, $\textbf{B}$, and $\textbf{C}$ are $2\times 2$ matrices, $\textbf{C}'$ is the transpose of $\textbf{C}$, and only elements $C_{ij}$ do depend on $x$ and go to 0 for $x\rightarrow \infty$. We may write $$\textbf{T}=\textbf{G}^{-1}\widetilde{\textbf{G}}=\textbf{I}+\varkappa\textbf{G}^{-1}\textbf{D}=
\textbf{I}+\varkappa
\begin{pmatrix}
    \textbf{A}       & \textbf{C} \\
    \textbf{C}'       & \textbf{B}
\end{pmatrix}
\begin{pmatrix}
    \textbf{d}       & \textbf{0} \\
    \textbf{0}       & \textbf{d}
\end{pmatrix},
\label{Ginf2}$$ here $\textbf{d}$ is a $2\times 2$ diagonal matrix having elements $d_{ii}=(-1)^{i-1}$. The final explicit form of matrix $\textbf{T}$ is presented in Appendix \[appA\].

Breakdown of the normal diffusive transport in the nondispersive transport regime
=================================================================================

General consideration
---------------------

Calculation of $\det\textbf{T}$ 