2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129610We study properties of a sequence $Λ$ obtained by a randomselection of integers $n$, where $n\inΛ$ with probability $\varpi_{n}$, independently of the other choices. We distinguish two cases : if $\limsup_{n\to\infty}n\varpi_{n}<\infty$, $Λ$ is a.s. a Sidon set, non-dense in the Bohr group ; if $\lim_{n\to\infty}n\varpi_{n}=\infty$, then $Λ$ is a.s. a set of analyticity and is dense in the Bohr group.Classical Analysis and ODEsProbability11K31; 11K70; 60G55text