**Date & Time:** Wednesday, April 13, 2016, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:**Jon Aaronson,

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.