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We extend previous results providing an exact formula for the variance of alinear statistic for the Jellium model, a one-dimensional model of Statisticalmechanics obtained from the $k \longrightarrow 0^{+}$ limit of the Dysonlog-gas. For such a computation of the covariance, in comparison to previouswork for computations of the log-gas covariance, we obtain a formula betweentwo linear statistics, given arbitrary functions $f$ and $g$ over the realline, that is dependent upon an asymptotic approximation of the Jelliumprobability distribution function from large $N$ deviations, and from aneffective saddle-point action.

A computation of the covariance between two linear statistics for the Jellium model