Date & Time: Wednesday, April 13, 2016, 16:00-17:00.
Venue: Ramanujan Hall
Tel Aviv University
Title: Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations
Abstract: In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem. I will give a review of the subject and then show that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation. This is deduced from the dual result that every random variable on the positive reals occurs as the distributional limit of the partial sums some positive, ergodic stationary process normalized by a 1-regularly varying normalizing sequence. Joint work in progress with Benjamin Weiss.