On the upper tail of star counts in random graphs

Margarita Akhmejanova, Matas Šileikis

Let $X$ count the number of $r$-stars in the random binomial graph $\mathbb{G}(n,p)$. We determine, for fixed $r$ and $\epsilon >0$, the asymptotics of $\log \mathbb{P}(X \ge (…