Consider a fixed tessellation of the plane into a countable set of polygonal cells \(A_{1}, \ldots\), and let \(0 \leq \ell_{i j}<\infty\) be the length of the common boundary \(\partial A_{i} \cap \partial A_{j}\). Associate with each ordered pair of regions \((i, j)\) a Gaussian random variable

\[
\varepsilon_{i j}=-\varepsilon_{j i} \sim N\left(0, \ell_{i j}ight)
\]

with independent and identically distributed signs independent of \(|\varepsilon|\). If all boundary lengths \(\ell_{i}\). are finite, the row sums \(W\left(A_{i}ight)=\varepsilon_{i}\). define a Gaussian process indexed by cells. Find the covariances \(\operatorname{cov}\left(W\left(A_{i}ight), \bar{W}\left(A_{j}ight)ight)\) for \(i=i\) and \(i eq j\).