Some Generic Properties of Processes
Dynamical Systems
2025-07-30 v1
Abstract
For a given ergodic measure preserving transformation T of a standard measure space each finite labelled partition defines an ergodic stationary process. There is a complete metric on the space of partitions which is separable. Various generic properties of these processes will be given. For example: 1. The generic partition defines a process that is not Rosenblatt mixing. 2. If T is a K-automorphism that is not Bernoulli then the generic partition is also K but not Bernoulli. Extensions to the relative setting and to actions of amenable groups will also be discussed.
Cite
@article{arxiv.2507.21620,
title = {Some Generic Properties of Processes},
author = {Benjamin Weiss},
journal= {arXiv preprint arXiv:2507.21620},
year = {2025}
}