Distributional Limits of Positive, Ergodic Stationary Processes and Infinite Ergodic Transformations

<strong>Mathematics Seminar of the School of Physical Sciences ---------------------------------------------------------</strong> Title: <strong>Distributional Limits of Positive, Ergodic Stationary Processes and Infinite Ergodic Transformations</strong> Speaker: <strong>Jonathan Aaronson </strong> (Tel Aviv University, Tel Aviv) Date: <strong>April 25, 2016</strong> <strong>Abstract:</strong> In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem. We will 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 will consider consequences in infinite ergodic theory: e.g., rational ergodicity properties. It follows 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 (and the process can be chosen over any EPPT).