New concentration inequalities for suprema of empirical processes
  While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive concentration inequalities assuming only low moments for an envelope of the empirical process. These concentration inequalities are beneficial even when the envelope is much larger than the single functions under consideration. 
Johannes Lederer, Sara van de Geer
math.PR math.ST stat.TH