An alternative approach to large deviations for the almost-critical Erdős-Rényi random graph

Luisa Andreis, Gianmarco Bet, Maxence Phalempin

We study the near-critical behavior of the sparse Erdős-Rényi random graph $\mathcal{G}(n,p)$ on $n\gg 1$ vertices, where the connection probability $p$ satisfies $np = 1+θ(b_n^2/n)…