  We study the model theory of expansions of Hilbert spaces by generic
predicates. We first prove the existence of model companions for generic
expansions of Hilbert spaces in the form first of a distance function to a
random substructure, then a distance to a random subset. The theory obtained
with the random substructure is {\omega}-stable, while the one obtained with
the distance to a random subset is $TP_2$ and $NSOP_1$. That example is the
first continuous structure in that class.
