A local limit theorem for the edge counts of random induced subgraphs of a random graph

Paul Balister, Emil Powierski, Alex Scott +1

Consider a `dense' Erdős--Rényi random graph model $G=G_{n,M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M/\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ is bounded away from 0 and 1. Fi…