Hausdorff dimension of affine random covering sets in torus
We calculate the almost sure Hausdorff dimension of the random covering set in -dimensional torus , where the sets are parallelepipeds, or more generally, linear images of a set with nonempty interior, and are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing.