Distributional limits of positive, ergodic stationary processes and   infinite ergodic transformations
  In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible.   Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and $\alpha$-rationally ergodic tranformations are presented. 
Jon. Aaronson and Benjamin Weiss
math.DS math.PR