Randomized coverings of a convex body with its homothetic copies, and   illumination
  We present a probabilistic model of illuminating a convex body by independently distributed light sources. In addition to recovering C.A. Rogers' upper bounds for the illumination number, we improve previous estimates of J. Januszewski and M. Nasz\'odi for a generalized version of the illumination parameter. 
Galyna Livshyts, Konstantin Tikhomirov
math.MG