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The asymptotic behavior as $N$ goes to infinity of correlation functions:\n  $$ \\mathfrak C_N(T)= \\mathbb E\\bigg[ \\prod_{(i,j) \\in T} \\Big(\\mathbf 1_{\\big(\\{i,j\\} \\in G_N \\big)} - \\mathbb P(\\{i,j\\} \\in G_N) \\Big)\\bigg], \\ T \\subset [N]^2 \\textrm{finite}$$ furnishes informations on the asymptotic spectral properties of the adjacency matrix $A_N$ of $G_N$. 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The asymptotic behavior as $N$ goes to infinity of correlation functions:\n  $$ \\mathfrak C_N(T)= \\mathbb E\\bigg[ \\prod_{(i,j) \\in T} \\Big(\\mathbf 1_{\\big(\\{i,j\\} \\in G_N \\big)} - \\mathbb P(\\{i,j\\} \\in G_N) \\Big)\\bigg], \\ T \\subset [N]^2 \\textrm{finite}$$ furnishes informations on the asymptotic spectral properties of the adjacency matrix $A_N$ of $G_N$. 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