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

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