A Local Central Limit Theorem for Clique Counts in Sparse Random Graphs

Asaf Cohen Antonir, Ilay Hoshen, Maksim Zhukovskii

Let $X_H$ denote the number of copies of a fixed graph $H$ in $G_{n,p}$. Gilmer and Kopparty conjectured that $X_H$ satisfies a local central limit theorem (LCLT) provided that $H…