Entiers al\'eatoires, ensembles de Sidon, densit\'e dans le groupe de Bohr et ensembles d'analyticit\'e

We study properties of a sequence $\mathrm{\Lambda }$ obtained by a randomselection of integers $n$, where $n\in \mathrm{\Lambda }$ with probability ${\varpi }_n$, independently of the other choices. We distinguish two cases : if ${\mathrm{lim\hspace{0.17em}sup}}_{n\to \mathrm{\infty }}n{\varpi }_n<\mathrm{\infty }$, $\mathrm{\Lambda }$ is a.s. a Sidon set, non-dense in the Bohr group ; if ${\lim }_{n\to \mathrm{\infty }}n{\varpi }_n=\mathrm{\infty }$, then $\mathrm{\Lambda }$ is a.s. a set of analyticity and is dense in the Bohr group.