Some Generic Properties of Processes

2025/07/29 by Weiss, Benjamin
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.21620

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.

Citations

• Facteurs disjoints des transformations melangeantes
• An ergodic system is dominant exactly when it has positive entropy
• On some generic classes of ergodic measure preserving transformations

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