On the visibility in well-behaved random sets in Euclidean space

In Calka et al. (2009), the decay of the probability of reaching distance at least r in some direction from a given point without hitting any ball, in the Poisson Boolean model of continuum percolation, was studied. The methods used in Calka et al. (2009) include coverage techniques, and the most precise results were obtained in dimension 2. In this note, we strengthen some of the results obtained in Calka et al. (2009) to dimension 3 and higher and at the same time extend them to more general random sets.