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In this paper we prove a quantiative local limit theorem for the distributionof the number of triangles in the Erd\H{o}s-Renyi random graph $G(n,p)$, for afixed $p\in (0,1)$. This proof is an extension of the previous work of Gilmerand Kopparty, who proved that the local limit theorem held asymptotically fortriangles. Our work gives bounds on the $\ell^1$ and $\ell^\infty$ distance ofthe triangle distribution from a suitable discrete normal.

A Quantitative Local Limit Theorem for Triangles in Random Graphs