Some properties of stationary determinantal point processes on Z
Résumé
We study properties of stationary determinantal point processes X on Z from different points of views. It is proved that X boolean AND N is almost surely Bohr-dense and good universal for almost everywhere convergence in L1, and that X is not syndetic but X+X=Z. For the associated centered random field, we obtain a sub-Gaussian property, a Salem-Littlewood inequality and a Khintchine-Kahane inequality.