Colloquium: Tuesday, June 7, 2 pm. Speaker: Jonathan Aaronson (Tel Aviv). Title: “Distributional limits of positive, ergodic stationary processes & infinite ergodic transformations”.

In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem.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.

We’ll consider consequences in infinite ergodic theory: e.g. rational ergodicity properties.

It follows from a duality technique (“inversion”) that every random variable on the positive reals occurs as the distributional limit of the partial sums of some positive, ergodic stationary process  normalized by a 1-regularly varying normalizing sequence (& the process can be chosen over any EPPT).

arXiv:1604.03218

Joint work with Benjamin Weiss