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Assume that $\\exp(-\\frac{1}{Ch}) < \\delta \\ll h^{\\kappa}$ for constants $C,\\kappa>0$ suitably large. Let $\\Sigma$ be the closure of the range of the principal symbol. We study the $2$-point intensity measure of the random point process of eigenvalues of the randomly perturbed operator $P_h^{\\delta}$ and prove an $h$-asymptotic formula for the average $2$-point density of eigenvalues. 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