= Critical-window connectivity probability of a binomial random graph
{title2=$\mathbb P(G(n,(\log n+c)/n)\text{ is connected})\to e^{-e^{-c}}$}
For fixed real $c$, the number of <isolated vertices> in a <binomial random graph> with $p=(\log n+c)/n$ converges to a <Poisson distribution> of mean $e^{-c}$. Its fixed <factorial moments> tend to $(e^{-c})^k$. A <union bound> for small <connected components>, together with exclusion of intermediate components, shows that <isolated vertices> are asymptotically the only obstruction to connectivity. Thus the displayed <limit> is the zero-mass of that <Poisson distribution>.
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