We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the $d$-dimensional torus. In metric spaces, we consider covering sets generated by balls and, in tori, we deal with general analytic generating sets.
"Hitting probabilities of random covering sets in tori and metric spaces." Electron. J. Probab. 22 1 - 18, 2017. https://doi.org/10.1214/16-EJP4658