A large-deviations principle for all the cluster sizes of a sparse Erdős-Rényi graph

Luisa Andreis, Wolfgang König, Robert I. A. Patterson

Let $\mathcal{G}(N,\frac{1}{N}{t}_N)$ be the Erdős-Rényi graph with connection probability $\frac{1}{N}{t}_N\sim t/N$ as $N\to \infty$ for a fixed $t\in (0,\infty )$. We derive a large-deviatio…