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We obtain Berry-Esseen-type bounds for the sum of random variables with adependency graph and uniformly bounded moments of order $\delta \in (2,\infty]$using a Fourier transform approach. Our bounds improve the state-of-the-art inthe regime where the degree of the dependency graph is large. As a Corollary ofour results, we obtain a Central Limit Theorem for random variables with asparse dependency graph that are uniformly bounded in $L^{\delta}$ for some$\delta\in(2,\infty]$.

Berry-Esseen-type estimates for random variables with a sparse dependency graph