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.
Categories: math.CA math.PR
