# Monday 20 Feb 2017: Dynamics Seminar: In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem.

### Jon Aaronson - Tel Aviv Univesity

H254 14:30-15:30

We'll review the subject and then see that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation.

As a corollary, we obtain a complete classification of the possible "A-rational ergodicity properties" (0 \lthan A \le infinity) for an infinite ergodic transformation.

The main construction follows by "inversion" from a cutting and stacking construction showing 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 (indeed, here the process can be chosen over any EPPT).