Ultrafilters in the random real model

We prove that $\mathsf{\text{P}}$-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than ${\mathrm{\aleph }}_{\omega }$-many random reals to a model of $\mathsf{\text{CH.}}$These results improve and correct previous theorems that can be found in the literature.