Limit laws for distorted return time processes for infinite measure   preserving transformations
  We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition. We identify two critical cases for which we prove uniform distribution laws. For this we introduce the notion of uniformly returning sets and discuss some of their properties. 
Marc Kesseb\"ohmer and Mehdi Slassi