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 \(\delta \in (2,\infty ]\) $\delta \in (2,\infty ]$ using a Fourier transform approach. Our bounds improve the state-of-the-art obtained by Stein’s method in the regime where the degree of the dependency graph is large.