  We study properties of a sequence $\Lambda$ obtained by a randomselection of
integers $n$, where $n\in\Lambda$ with probability $\varpi_{n}$, independently
of the other choices. We distinguish two cases : if
$\limsup_{n\to\infty}n\varpi_{n}<\infty$, $\Lambda$ is a.s. a Sidon set,
non-dense in the Bohr group ; if $\lim_{n\to\infty}n\varpi_{n}=\infty$, then
$\Lambda$ is a.s. a set of analyticity and is dense in the Bohr group.
