Hausdorff dimension of random covering sets generated by balls

We consider the Hausdorff dimension of random covering sets generated by balls and driven by general measures. We improve a lower bound given by Ekström and Persson in 2018, extend it to generating balls with an arbitrary sequence of radii and prove their conjecture concerning the exact value of dimension in the special case of radii $n^{-\alpha}$ for a certain parameter range. Further, we show that the natural extension of the conjecture is not true for generating balls with an arbitrary sequence of radii. We also give various examples demonstrating the complexity of dimension in this general case. The talk is based on joint work with Esa Järvenpää, Maarit Järvenpää and Örjan Stenflo.