Consider simple, undirected Erdős–Rényi graphs $G(n,p)$, where $n$ is the number of vertices and $p$ is the probability any pair of vertices form an edge. Many properties of these graphs are known - in particular, $G(n,p)$ is almost surely connected when $p \gt \frac{n}{log(n)}$, and the largest clique in $G(n, \frac{1}{2})$ is almost surely about 2log$_2$(n).

What is known about the vertex connectivity number $\kappa(G)$, $G\in G(n,p)$, the minimum number of vertices that one must remove in order to disconnect the graph?

It is known that for fixed $k$ and fixed $p\in (0,1)$, almost every graph in $G(n,p)$ is k-connected, but what is the expected connectivity as a function of $p$ and $n$?